It's important to separate operational deficiencies that probably led to MySpace's decline from product and feature choices.  It's possible to argue that their products and feature simply didn't fit the market, but for the purposes of this answer I will assume that there was/is a market for MySpace's particular product offering (e.g. anonymity) and that their decline is due largely to operational factors (e.g. poor technology).

In my opinion, here are some major contributing factors:

• Inability to recruit top-tier talent. MySpace suffered a stigma of being a trivial entertainment-oriented site and, increasingly as time wore on, a cultural ghetto.  Facebook suffered from similar image problems of not being a very serious place to work, but was eventually able to overcome this by promoting its brand of being a technological powerhouse.  Also, MySpace was headquartered in Los Angeles, far from the talent center of Silicon Valley, so the available recruiting pool was that much smaller.  The compounding effects of this (top people attract other top people) exacerbated this problem over time.  This manifested itself not just in technological sophistication but also in terms of how innovative or driven its internal culture ended up developing.
• Corporate parent.  Organizations that belong to a larger corporate parent often find themselves unable to focus squarely on strategies or actions which benefit them, because the corporate parent has other overriding priorities.  One way in which this seemed to interfere with MySpace's operations is that revenue and advertising priorities set by the corporate parent (News Corporation) would cause them to take decisions that degraded the user experience or product value delivered to users.  This kept them from executing an optimal strategy to appeal to users.
• Reliance on closed-source technology stack.  This is not normally a problem in most companies, but in companies where the technical operations are world-class in size and scale, it becomes necessary to be able to directly develop and extend the technologies being used since the scale of the operation means that new technological ground is constantly being broken.  Closed-source OTS technology (even with direct on-site assistance from the vendor) places the company at the mercy of the vendor, who implicitly lacks as strong a motivation to solve key scalability challenges because it is not their core business (it's just another vendor, albeit an important one).  The vendor may also lack the ability to extend their technology to the scale at which it is being used, and will resist attempts to evaluate whether their technology should be replaced or re-written.

I think the main problem was too much friction in the browsing experience on MySpace. The main source of this friction was the profile page, which gave user's more freedom of expression than Facebook's profile walls, but ultimately took far too long to load, crashed people's browsers and meant that the UI elements constantly changed from profile to profile.

Most users care more about the browsing experience more than creative expression and the rest either found that their friends had left for Facebook (or never joined MySpace in the first place) or moved to blogging sites like tumblr which give users the best of both worlds for the minority that care more about creative expression than a complete social graph (where Facebook now has a huge advantage over all the other networks).

I think even if MySpace had recruited more engineering talent they would still have been reluctant to kill the profile pages as this would have upset many of their most frequent users who spent so much time creating their profiles (on a side note, MySpace deserves credit for teaching millions basic html/ css skills as a result of this).

Facebook on the other hand seems to have no problem upsetting their users on a regular basis to make necessary changes to their UI to remain competitive against startups like twitter, tumblr and friendfeed.

Rather than lack of engineering talent (this slowed their development down, but if they had been building the right product I think their huge advantage in user numbers would have given them enough of a headstart to stay ahead), their parent company (which gave them huge financial advantages) or closed source technology (an identical site built in PHP might be faster, but would still have the same UI problems) I think the main problem was really that they built their product for their most active users rather than asking themselves which products they needed to build to attract new users and engage inactive users. Facebook on the other hand seem to pay more attention to the popular features of their competitors than the requests of their active users.

As a complement to Yishan Wong's answer, I'm going to assume that their infrastructure and operational issues were not the cause of their decline and focus on the product.  There are three big things that held them back. 

• The site is unusable.  People will not put up with a bad product forever no matter how strong the network effects.  The most blatant example is its layout.  There is no logic to MySpace's core navigation.  There are links everywhere, and the design lends no clues as to what I should be doing.  Each page lets every element fend for itself, competing for attention and clicks.  The core navigation changes from page to page.  Go to 50 Cent's page ( http://myspace.com/50cent ); good luck getting back to the home page. 
• They love advertisers more than they love users.  They overoptimize for the advertiser's experience to the point where it's just embarrassing.  Even if you're logged in, going to myspace.com takes you to the splash page with the big ad of the day (one time, they sold an Incredible Hulk ad where the Hulk jumped out at you -- no joke).  When viewing a profile, the advertisements are more prominent than the person's picture.  There are at least 3 big visual ads on every page. 
• Why fix it if it's making money?  I'm pretty sure their focus on advertisers has gotten in the way of innovation and staying relevant.  For example, I can't imagine them forcing a consistent navigation on every page to make a better user experience.  What would 50 Cent's label say?  So now MySpace is stuck as a company that hosts custom landing pages until the ad dollars demand something new.

I was at Intermix, MySpace and FIM for over 5 years.
There is one and only one reason MySpace "fell so far, so fast":
It did not continually evolve the product and roll out features fast enough or in a regular way. They did ship product, but they just didn't do it as fast as Facebook. In the consumer internet space, "shipping product" is the key to competing. No matter what you think of Facebook and Google products, these companies are leaders in the space because they are extraordinary and prolific at shipping products.

While many believe UI clutter, annoying personalization, lack of true identity, privacy, or ads killed MySpace, these factors are marginal at best. For every one of these factors I can name a successful consumer internet company today that has one or more of these issues and is thriving. For example, have you ever looked at some of the Twitter or Tumblr backgrounds users employ? Have you ever looked at some of usernames of many active Twitter accounts?

The people who think these issues caused the decline are mostly speaking from a personal preferences point of view and are not in touch with regular everyday users. These issues are mostly inside baseball. Recently, I was having dinner and talking with my teenage niece and nephews about social media. I asked them what they and their friends wanted most out of Facebook. Their reply: personalization and ability to customize their pages a la MySpace. LOL! They also think the Facebook PC UI is too complicated and prefer to use Facebook on their iPhones. I asked "Do most people in your school feel this way?" My nephews answer, "Yep, I haven't logged into Facebook on a PC in 4 months." Of course this purely anecdotal, but I don't think its unusual for this demo.  The point here is: different things are pet peeves for different users, but the one sure way to alienate and lose all of your users is to NOT improve your product.

To date, the only person Ive seen get this analysis correct is Sean Parker
http://www.pcmag.com/article2/0,...

In addition to Yishan Wong and Peter Deng's great answers, I would add that MySpace focused very heavily on a specific demographic (young, alternative music-lovers) that influenced the design of their property in a direction away from the mass-market.  MySpace's user pages tend to be very chaotic and edgy, very unlike the order that Facebook brings to their user's profiles.  By successfully focusing on their early adopter demographics their user experience left the rest of the market.  This may be a function of being in Los Angeles and being focused on music and entertainment, but it's clear they missed a much larger community opportunity.

MySpace put way to much emphasis on form ("Everyone Can Customize Their Own Backgrounds!") and not enough emphasis on function (making it seamless to connect, share, and socialize with friends)

Good Technology, good UI, should be invisible. Less is more (ask Steve Jobs).

Function should take precedence over form, at least in the initial of product dev. Eventually, the two should balance each other out (again, see Steve Jobs). But Function must always take the lead.

You could make a car dashboard with gold trim, blinking lights, and velvet purpose buttons, but if don't know how to turn the damn radio on, what good is it?

With MySpace, Form was always front in center: blinking graphics, large image post, and inconsistent UI. The user spent more time on the form (distracting visuals) and less time on the function (connecting and socializing).

Facebook took the opposite apporach: The UI was a means to an end (faciliating social connects) and not an end of itself ("You can make your profile pic an animated gif!").

All the other stuff above is valid, but at the end of the day, MySpace messy, inconsistent UI made a less effective social utility when compared to Facebook, IMHO.