1) GoogleThere was as time when you knew your friend's and family member's phone numbers. There may have been a time when you knew the addresses of people you emailed a lot. And there was a time when I knew how to get across town without using my navigator. Software has taken over these jobs from our brains, because it's better at it. Domain names are like phone numbers and email addresses—unique identifies that allow computers to disambiguate from the more natural (but likely non-unique) handles our brains like. (Put aside that domain names are actually the human readable system for IP addresses. They're still computery.)
If you start typing "bob" into the To: field in your email client, it will give you some choices of the Bob's you've emailed before, which is almost always good guess. If it's wrong, you go look up the address and then probably copy+paste it in without really paying attention to what it is.
A lot of people use Google this same way. The first time how saw how often people got to Yahoo by typing yahoo.com into Google, I was shocked. And as this famous comment thread shows—where thousands of Facebook users showed up to a blog post talking about Facebook logins and got confused because typing "facebook login" into Google was how they got there—Google is how normal people get around the web. This probably wouldn't be true if Google wasn't so damn fast. But it is. It's the auto-complete of the web. Well, one of them...
2) Auto-Complete Address BarsFor those slightly more sophisticated users, the auto-complete/suggest feature in browser address bars saves our brain from remembering domains once we've been there once or twice. In fact, with Chrome, Google has combined the search box and the address bar in such a beautiful way, that you don't really have to remember anything.
3) Mobile Web Browsers and Hidden Address BarsOne thing that keeps our awareness on domains is that we see them at the top of every web page we go to. However, this isn't as true when browsing the web from your mobile device. Because of space constraints, the address bar is more often hidden. You also don't have the status bar at the bottom that we're all used to looking at when hovering over a link to see what domain it goes to.
For the sake of simplicity and minimalism, Google may even bring the hidden address bar to the desktop browser. (The more I write this, the more I wonder if Google has a secret plan to kill domain names all together and make sure all navigation goes through them. Note to self: Start a conspiracy about that.)
4) AppsAbove, I'm still talking about web usage on the phone. But a reason a lot of people are less concerned about domains these days is, of course, installable apps. Personally, I'm not a "the future is all about apps" sort of guy. But clearly their usage is significant, and it eats into web usage. While almost every app has a web site of some sort, the domain name is very unimportant when most of app discovery is through stores.
5) Alternative SuccessesThe last reason getting the perfect .com is less important than it used to be is simply because others have proven you can succeed without it. A good domain name is a signal of legitimacy. As far as I know, there have been no big internet properties with .biz or .cc names. You know when you see one that it's suspect. However, you no longer necessarily suspect some alternative domains.
Del.icio.us was a pioneer of the domain hack and had lots of geek cred (though Yahoo, wisely, ponied up for the real deal, cuz that this was hard to type). Bit.ly popularized the .ly space, now used by a bunch of startups. About.me embraced the alternative domain as part of its name, as did Last.fm and the new hotness, turntable.fm. (I'm sure I'm forgetting many other examples.)
The non-perfect .com is also acceptable these days. After all, Facebook used to be at thefacebook.com. Dropbox was getdropbox.com. While those have since upgraded, their success was not predicated on that, obviously. 37 Signals was one of the earliest well-respected players to say, Screw it, the product is called Basecamp, but the domain is basecamphq.com. You see this kind of thing on well-designed, well-branded products more and more.
Because of these examples, the expectations change.
I don't know what will happen with the new TLDs that are to be issued. I suspect we'll just see more non-dot-com successes, which will open up the possibilities more. Which is a good thing for creators and entrepreneurs who don't have the dough to pay for the perfect .com even if wasn't being used and they could track down the owner and go through some onerous negotiation process. (Shouldn't it be easier?)
Conclusion: Names are more important than domain namesWhile a good .com name is still worth a lot, it's not as crucial to success on the internet as it used to be. And the forces that have made it less important will continue to make it less important over time (especially the mobile-related ones). I'd still opt (and pay up) for a nice, clean .com if I could get one, but I wouldn't consider it a must have.
Product and brand names, on the other hand, are just as important as ever (or more so in an increasingly crowded internet). Too many startups have suffered a stupid name to get the domain that fit. Hopefully, entrepreneurs will feel less pressure to do that as the world becomes more auto-complete/app/mobile driven and less-dot-com biased.