I know, this question has been answered thousands of times. Even still, nobody can agree on what it is exactly. Here's my take.
Web 2.0 obviously implies the "next version" of the web. Ask Tim O'Reilly (who coined the term to promote a conference), and he won't really be able to summarize it either. He'd rather define it by example. DoubleClick is Web 1.0, Google Adsense is Web 2.0. Personal websites are Web 1.0, blogs are Web 2.0. Content Management Systems were Web 1.0, wikis are Web 2.0.
Web 2.0 is said to include everything from tagging, Ruby on Rails, AJAX, peer-to-peer, RSS, the perpetual Beta, and user-contributed data. Let me propose this: Web 2.0 includes anything that was done successfully on the web in 2005. There, I've said it. Now, I'd like to propose something else: Let's focus on the different ways the web has improved, and let's never use the term Web 2.0 again. Seriously, starting right now. Who's with me?
Having said all this, the many different definitions can finally be read without that nauseous feeling. Don't worry any longer that your website is running the wrong version of the Internet, just relax and take a look at how far we've come. It's not worth much to say "This website follows the new trends in web sites, this one doesn't". There's certainly no need to start a new industry over it. Instead, let's just see what works and what doesn't.
If we spend all our time defining such a vague marketing term, we're going to severely miss the point. There is no Web 3.0, and there needn't be a Bubble 2.0. We have a lot of really great examples to follow, and there's still a lot that hasn't been done. So let's just keep doing what we do best.