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Use of JavaScript in lieu of hyperlinks

As RIAs and SPAs (or web apps with heavy javascript usage) have become more and more popular, I've been running into systems that, instead of using good old a href hyperlinks, I see them utilizing constructs using onclick with JavaScript code that manipulates navigation. This is particularly true with images.
For example, instead of seeing something like this:
<img src="...."/>
<div ... onclick='SomeJsFunctionThatNavsToAnotherPage()'><img src="..."/></a>
What is the advantage of this? It makes it incredibly hard to trace where pages transition to when debugging or trying to root cause a bug. I can get the idea when the target to navigate can change (so yes, here you could use a function that computes to what page to navigate to.)
But I see this pattern even when the pages to navigate to are constant. I find this extremely convoluted and hard to test. Not to mention that there is always the browser-specific bugs that come from stuff (sadly in my experience from over-complexifying the front-end.)
But I am not a RIA/SPA developer (just backend and traditional web development). Am I missing the rationale behind this?
TO CLARIFY
My question is not for the case when we want to redraw the page or change current content without changing the current location. My question is for plain
old transitions, from page A to page B.
In such a case, why use onclick=funcToChangeLocation() over <a href="some location"/>.
This has been a pain for me when troubleshooting systems that are already written (for I wouldn't write them like that), but there could be reasons I am not aware of.
Again, my question is not for pages that redraw themselves without changing the browser location, but for navigation from one page to the next.
ALSO
If you are going to vote to close this question, at least leave a message explaining why.

If you are making a web application, sometime you don't want to redirect the user to another page, but you want to dynamically change the content of the page without refreshing the page. It has some advantages. It can be faster. You can easily keep the state of the page/application. You are not obligated to communicate with the server. You can update only a part of the page.
You can also dynamically request data to print the page. If you are displaying an user profile page, you can only ask a json object that represent the user. This json object is smaller than the whole page and will be dynamically rendered. It can help to reduce the data transfer between users and server when your bandwidth is limited.
EDIT: In the case of a simple page redirection, I think it's a bad practice and I cannot see an advantage. I think it obfuscate the website when the google crawler try to parse the website.

I once had a pretty successful web directory website. One day Google decided that "directories" are competing businesses and started penalizing sites that had links on directories. I used the method you describe to cloak outgoing links to try and trick Google.

Cramming tons of HTML in to one page

I am helping to design a HTML client for a game that I am collaborating with others on.
This client is going to need to have multiple scenes/pages like the login, the lobby, the actual game page, etc.
Normally, I would be just fine with navigating in and out of pages. However, the client needs to have a constant connection with the server via a Websocket, so therefore it cannot navigate away from the page.
Option 1: Put everything in one file
Rather than having each scene in its own separate page, just cram all the HTML together.
Then, when one scene is needed, simply hide all the other scenes.
I do not think that this way is the way to go: from what I know about HTML and web practices, this is not a very smart practice.
Option 2: jQuery's .load()
Using jQuery's handy-dandy .load method, an external HTML file can be easily loaded into the current HTML file.
To me, this seems that this might be the best way. However, I am not very familiar with how this method acts, so I do not know if this will cause bumps in the road ahead.
Option 3: ???
This is where I need help. Unless one of the two above options is the best way, what is the best option for my situation?
Notes
I am not looking for speed here; it's okay if there is some delay between loads.

Not sure about your backend but it seems like you are looking for a single page app solution.
I recommend AngularJS, currently maintained by Google.

Others have mentioned Angular, but I'll just throw out the recommendation of KnockoutJS as well. Knockout has a less steep learning curve than AngularJS, and though it doesn't have as many features as Angular does, the latest version does have better browser support.
Both Knockout and Angular have excellent documentation and tutorials available via their websites.

I would recommend Angular 2. Since you seem like a beginner in front-end (correct me if I am wrong), starting with Angular 2 would be great over 1 because then you can learn this really good JS framework only once. It will help you keep everything organized and will prevent you from making your markup messy.

Should I render this template using JavaScript or the server?

I'm rendering a news feed.
I'm planning to use Backbone.js for my javascript stuff because I'm sick of doing manual DOM binds with JQuery.
So right now I'm looking at 2 options.
When the user loads the page, the "news feed" container is blank. But the page triggers a javascript which renders the items of the news feed onto the screen. This would tie into Backbone's models and collections, etc.
When the user loads the page, the "news feed" is rendered by the server. Even if javascript was turned off, the items would still show because the server rendered it via a templating engine.
I want to use Backbone.js to keep my javascript clean. So, I should pick #1, right?? But #1 is much more complicated than #2.
By the way, the reason I'm asking this question is because I don't want to use the routing feature of Backbone.js. I would load each page individually, and use Backbone for the individual items of the page. In other words, I'm using Backbone.js halfway.
If I were to use the routing feature of Backbone.js, then the obvious answer would be #1, right? But I'm afraid it would take too much time to build the route system, and time should be balanced into my equation as well.
I'm sorry if this question is confusing: I just want to know the best practice of using Backbone.js and saving time as well.

There are advantages and disadvantages to both, so I would say this: choose the option that is best for you, according to your requirements.
I don't know Backbone.js, so I'm going to keep my answer to client- versus server-side rendering.
Client-side Rendering
This approach allows you to render your structure quickly on the server-side, then let the user's JavaScript pick up the actual content.
Pros:
Quicker perceived user experience: if there's enough static content on the initial render, then the user gets their page back (or at least the beginning of it) quicker and they won't be bothered about the dynamic content, because in all likelihood that will render reasonably quickly too.
Better control of caching: By requiring that the browser makes multiple requests, you can set up your server to use different caching headers for each URL, depending on your requirements. In this way, you could allow users to cache the initial page render, but require that a user fetch dynamic (changing) content every time.
Cons:
User must have JavaScript enabled: This is an obvious one and I shouldn't even need to mention it, but you are cutting out a (very small) portion of your user base if you don't provide a graceful alternative to your JS-heavy site.
Complexity: This one is a little subjective, but in some ways it's just simpler to have everything in your server-side language and not require so much back-and-forth. Of course, it can go both ways.
Slow post-processing: This depends on the browser, but the fact is that if a lot of DOM manipulation or other post-processing needs to occur after retrieving the dynamic content, it might be faster to let the server do it if the server is underutilized. Most browsers are good at basic DOM manipulation, but if you have to do JSON parsing, sorting, arithmetic, etc., some of that might be faster on the server.
Server-side Rendering
This approach allows the user to receive everything at once and also caters to browsers that don't have good JavaScript support, but it also means everything takes a bit longer before the browser gets the first <html> tag.
Pros:
Content appears all at once: If your server is fast, it will render everything all at once, and that's that. No messy XmlHttpRequests (does anyone still use those directly?).
Quick post-processing: Just like you wouldn't want your application layer to do sorting of a database queryset because the database is faster, you might also want to reserve a good amount of processing on the server-side. If you design for the client-side approach, it's easy to get carried away and put the processing in the wrong place.
Cons:
Slower perceived user experience: A user won't be able to see a single byte until the server's work is all done. Sure, the server is probably going to zip through it, but it's still a few extra seconds on the user's side and you would do them a favor by rendering what you can right away.
Does not scale as well because server spends more time on requests: It might be that you really want the server to finish a request quickly and move on to the next connection.
Which of these are most important to your requirements? That should inform your decision.

I don't know backbone, but here's a simple thought: if at all possible and secure, do everything on the client instead of the server. That way the server has less work to do and can therefore handle more connections and scale better.

But #1 is much more complicated than #2.
Not really. Once you get your hang of Backbone and jQuery and client-side templating (and maybe throw CoffeeScript into the mix, too), then this is not really difficult. In fact, it greatly simplifies your server code, as all the display-related functions are now removed. You could also even have different clients (mobile version, for example) running against the same server.
Even if javascript was turned off, the items would still show because the server rendered it via a templating engine.
That is the important consideration here. If you want to support users without Javascript, then you need a non-JS version.
If you already have a non-JS version, you can think about if you still need the "enhanced" version, and if you do, if you want to re-use the server-side templating you already have coded and tested and need to maintain anyway, or duplicate the effort client-side, which adds development cost, but as you say may provide a superior experience and lower the load on the server (although I cannot imagine that fetching rendered data versus fetching XML data makes that much of a difference).
If you do not need to support users without Javascript, then by all means, render on the client.

I think Backbone's aim is to organize a Javascript in-page client application. But first of all you should take a position on the next statement:
Even if javascript was turned off, the web-app still works in "post-back mode".
Is that one of your requirements? (This is not a simple requirement.) If no, then I'll advice you: "Do more JS". But if yes then I believe your best friend is jQuery load function.
A Note: I'm a Java programmer and there's a lot of server-side frameworks that bring the ability to write applications that work ajax-ly when js is enabled and switch on post-backs when it isn't. I think Wicket and Echo2 are two of them but it's meant they are server-side libraries...

jQuery Mobile - all pages in index.html vs. single external pages - What gives better performance?

"The jQuery Mobile "page" structure is optimized to support either single pages, or local internal linked "pages" within a page." jQuery docs
What gives better performance for a jQuery Mobile application - which runs on PhoneGap?
all pages in a single.html file and internal loading
either single pages with external links
Any other aspects to consider?

I use jQuery mobile, and all the sites that I've made have been one page sites. The only external pages that I create are those that have embedded Google maps, just so the iframe loading doesn't happen if the user doesn't need it.
I think it boils down to this: one page with lots of content may slow initial loading but will be snappier once loaded, whereas a tiny home page will be quick from the start, buteach linked page will trigger an Ajax request. When designing for mobile, my rule of thumb is to minimize http requests as much as possible. Though many users are on 3+ G networks, it can still be a wait depending on connectivity. Also, connectivity can change in an instant and if the user has been navigating through the site successfully, and all of sudden things slow down to a crawl, this may create a bit of frustration. Therefore, I think from a user experience POV, users are willing to wait a few extra ticks on the initial load if everything else is quick once it's loaded.
Designing all in one page is also good for development with jQM, imo, because I just create a cache-manifest that includes only one page (and the css and js files). Then my site is cached and runs even if the user has no connectivity. If you've worked with applicationCache, you quickly realize that the more files you have, the more difficult it is to maintain the cache manifest and updates are slower.

I can't say much about browser performance, but you should consider load times.
Multiple pages in one document are loaded with the document, so if there's more of them, the DOMready will happen after some time, which can give an unpleasant look. Separate pages are fethed when you need them, so if there are no reasons to use multipage, then I'd recommend sticking with multiple HTML files. For an online app
Also - a multipage can't be used much if you want to stick with progressive enhancement which is JQM's development philosophy.
Any other aspects to consider?
Yes... As far as I know, there still might be some problems (eg. with dialogs) in multipage documents. JQMalpha3 didn't want to display dialogs for me if there was more than one in a multipage.

This depends on your app's size personally I've realised that using one page apps is more responsive if you have only a few pages in my case it was only 3 screens loading in external data which was more responsive than 3 seperate pages.
Hope that helps

Just In General: JS Only Vs Page-Based Web Apps

When a developing a web app, versus a web site, what reasons are there to use multiple HTML pages, rather than using one html page and doing everything through Javascript?
I would expect that it depends on the application -- maybe -- but would appreciate any thoughts on the subject.
Thanks in advance.
EDIT:
Based on the responses here, and some of my own research, if you wanted to do a single-page, fully JS-Powered site, some useful tools would seem to include:
JQuery Plug Ins:
JQuery History:
http://balupton.com/projects/jquery-history
JQuery Address:
http://plugins.jquery.com/project/jquery-address
JQuery Pagination:
http://plugins.jquery.com/project/pagination
Frameworks:
Sproutcore
http://www.sproutcore.com/
Cappucino
http://cappuccino.org/
Possibly, JMVC:
http://www.javascriptmvc.com/

page based applications provide:
ability to work on any browser or device
simpler programming model
they also provide the following (although these are solvable by many js frameworks):
bookmarkability
browser history
refresh or F5 to repeat action
indexability (in case the application is public and open)

One of the bigger reasons is going to be how searchable your website is.
Doing everything in javascript is going to make it complicated for search engines to crawl all content of your website, and thus not fully indexing it. There are ways around this (with Google's recent AJAX SEO guidelines) but I'm not sure if all search engines support this yet. On top of that, it's a little bit more complex then just making separate pages.
The bigger issue, whether you decide to build multiple HTML pages, or you decide to use some sort of framework or CMS to generate them for you, is that the different sections of your website have URL's that are unique to them. E.g., an about section would have a URL like mywebsite.com/about, and that URL is used on the actual "about" link within the website.

One of the biggest downfalls of single-page, Ajax-ified websites is complexity. What might otherwise be spread across several pages suddenly finds its way into one huge, master page. Also, it can be difficult to coordinate the state of the page (for example, tracking if you are in Edit mode, or Preview mode, etc.) and adjusting the interface to match.
Also, one master page that is heavy on JS can be a performance drag if it has to load multiple, big JS files.

At the OP's request, I'm going to discuss my experience with JS-only sites. I've written four relevant sites: two JS-heavy (Slide and SpeedDate) and two JS-only (Yazooli and GameCrush). Keep in mind that I'm a JS-only-site bigot, so you're basically reading John Hinkley on the subject of Jody Foster.
The idea really works. It produces gracefully, responsive sites at very low operational costs. My estimate is that the cost for bandwidth, CPU, and such goes to 10% of the cost of running a similar page-based site.
You need fewer but better (or at least, better-trained) programmers. JavaScript is an powerful and elegant language, but it has huge problems that a more rigid and unimaginative language like Java doesn't have. If you have a whole bunch of basically mediocre guys working for you, consider JSP or Ruby instead of JS-only. If you are required to use PHP, just shoot yourself.
You have to keep basic session state in the anchor tag. Users simply expect that the URL represents the state of the site: reload, bookmark, back, forward. jQuery's Address plug-in will do a lot of the work for you.
If SEO is an issue for you, investigate Google Ajax Crawling. Basically, you make a very simple parallel site, just for search engines.
When would I not use JS-only? If I were producing a site that was almost entirely content, where the user did nothing but navigate from one place to another, never interacting with the site in a complicated manner. So, Wikipedia and ... well, that's about it. A big reference site, with a lot of data for the user to read.

modularization.
multiple files allows you to mre cleanly break out different workflow paths and process parts.
chances are your Business Rules are something that do not usually directly impact your layout rules and multiple files would better help in editing on what needs to be edited without the risk of breaking something unrelated.

I actually just developed my first application using only one page.
..it got messy
My idea was to create an application that mimicked the desktop environment as much as possible. In particular I wanted a detailed view of some app data to be in a popup window that would maintain it's state regardless of the section of the application they were in.
Thus my frankenstein was born.
What ended up happening due to budget/time constraints was the code got out of hand. The various sections of my JavaScript source got muddled together. Maintaining the proper state of various views I had proved to be... difficult.
With proper planning and technique I think the 'one-page' approach is a very easy way to open up some very interesting possibilities (ex: widgets that maintain state across application sections). But it also opens up many... many potential problem areas. including...
Flooding the global namespace (if you don't already have your own... make one)
Code organization can easily get... out of hand
Context - It's very easy to
I'm sure there are more...
In short, I would urge you to stay away from relying on JavaScript dependency for the compatibility issue's alone. What I've come to realize is there is simply no need rely on JavaScript to everything.
I'm actually in the process of removing JavaScript dependencies in loo of Progressive Enhancement. It just makes more sense. You can achieve the same or similar effects with properly coded JavaScript.
The idea is too...
Develop out well-formatted, fully functional application w/o any JavaScript
Style it
Wrap the whole thing with JavaScript
Using Progressive Enhancement one can develop an application that delivers the best possible experience for the user that is possible.

For some additional arguments, check out The Single Page Interface Manifesto and some (mostly) negative reaction to it on Hacker News (link at the bottom of the SPI page):
The Single Page Interface Manifesto: http://itsnat.sourceforge.net/php/spim/spi_manifesto_en.php

stofac, first of all, thanks for the link to the Single Page Interface (SPI) Manifesto (I'm the author of this boring text)
Said this, SPI != doing everything through Javascript
Take a look to this example (server-centric):
http://www.innowhere.com/insites/
The same in GAE:
http://itsnatsites.appspot.com/
More info about the GAE approach:
http://www.theserverside.com/news/thread.tss?thread_id=60270
In my opinion coding a complex SPI application/web site fully on JavaScript is very very complex and problematic, the best approach in my opinion is "hybrid programming" for SPI, a mix of server-centric for big state management and client-centric (a.k.a JavaScript by hand) for special effects.

Doing everything on a single page using ajax everywhere would break the browser's history/back button functionality and be annoying to the user.

I utterly despise JS-only sites where it is not needed. That extra condition makes all the difference. By way of example consider the oft quoted Google Docs, in this case it not only helps improve experiences it is essential. But some parts of Google Help have been JS-only and yet it adds nothing to the experience, it is only showing static content.
Here are reasons for my upset:
Like many, I am a user of NoScript and love it. Pages load faster, I feel safer and the more distracting adverts are avoided. The last point may seem like a bad thing for webmasters but I don't want anyone to get rewarded for pushing annoying flashy things in my face, if tactless advertisers go out of business I consider it natural selection.
Obviously this means some visitors to your site are either going to be turned away or feel hassled by the need to provide a temporary exclusion. This reduces your audience.
You are duplicating effort. The browser already has a perfectly good history function and you shouldn't need to reinvent the wheel by redrawing the previous page when a back button is clicked. To make matters worse going back a page shouldn't require re-rendering. I guess I am a student of If-it-ain't-broke-don't-fix-it School (from Don't-Repeat-Yourself U.).
There are no HTTP headers when traversing "pages" in JS. This means no cache controls, no expiries, content cannot be adjusted for requested language nor location, no meaningful "page not found" nor "unavailable" responses. You could write error handling routines within your uber-page that respond to failed AJAX fetches but that is more complexity and reinvention, it is redundant.
No caching is a big deal for me, without it proxies cannot work efficiently and caching has the greatest of all load reducing effects. Again, you could mimic some caching in your JS app but that is yet more complexity and redundancy, higher memory usage and poorer user experience overall.
Initial load times are greater. By loading so much Javascript on the first visit you are causing a longer delay.
More JavaScript complexity means more debugging in various browsers. Server-side processing means debugging only once.
Unfuddle (a bug-tracker) left a bad taste. One of my most unpleasant web experiences was being forced to use this service by an employer. On the surface it seems well suited; the JS-heavy section is private so doesn't need to worry about search engines, only repeat visitors will be using it so have time to turn off protections and shouldn't mind the initial JS library load.
But it's use of JS is pointless, most content is static. "Pages" were still being fetched (via AJAX) so the delay is the same. With the benefit of AJAX it should be polling in the background to check for changes but I wouldn't get notified when the visible page had been modified. Sections had different styles so there was an awkward re-rendering when traversing those, loading external stylesheets by Javascript is Bad Practice™. Ease of use was sacrificed for whizz-bang "look at our Web 2.0" features. Such a business-orientated application should concentrate on speed of retrieval, but it ended up slower.
Eventually I had to refuse to use it as it was disrupting the team's work flow. This is not good for client-vendor relationships.
Dynamic pages are harder to save for offline use. Some mobile users like to download in advance and turn off their connection to save power and data usage.
Dynamic pages are harder for screen readers to parse. While the number of blind users are probably less than those with NoScript or a mobile connection it is inexcusable to ignore accessibility - and in some countries even illegal, see the "Disability Discrimination Act" (1999) and "Equality Act" (2010).
As mentioned in other answers the "Progressive Enhancement", née "Unobtrusive Javascript", is the better approach. When I am required to make a JS-only site (remember, I don't object to it on principle and there are times when it is valid) I look forward to implementing the aforementioned AJAX crawling and hope it becomes more standardised in future.