I found this highly viral video on GigaOM - What Is Web 2.0? Nokia Says Connecting People but I was thinking - since connecting with people was always the point, anyway (as the end of the video states) where's the Web 2.0 (I can't seem to embed the video here)?  Om Malik writes:

"…Given that everyone has tried their hand at defining Web 2.0, there is no harm in hearing out Nokia’s interpretation of Web 2.0. They obviously look at it from the point of view of mobile phones, and have produced a fun video to get their point across. Check it out, and let me know what you think."

I think Web 2.0 is typified in how applications talk to each other - for example, if I'm Twittering it now shows up in my news feed on Facebook and if I'm using Seesmic to post a video, my post shows up in on my Twitter feed as a tweet. Other examples might be OpenID (when it's fully functionally) that allow me to join new Social Networks while importing the friends I already have (or notifying them and asking them if they want to join as well).

One thing about Web 2.0, as defined the way I'm doing it, - it's much harder to track applications talking to each other than a Web 1.0 website - IE: your vanilla homepage, or even a site with Flash on it - sure, you have to work hard to embed tracking code, but once you do that, your pretty much enabled the metrics collection process.   With Web 2.0 (and we're not even into Web 3.0 yet) communication across web services - much harder to get a comprehensive idea of how a communication is traced across services.

I think the ideas I've heard IE: from Seth Godin, for example, where your looking for a flight and the applications know where your going and only show you the information very specific to your trip is an one example (weather you call it Web 2.0, Web 3.0 or Web 4.0) - you don't see that many Web Services (in this case, applications) that neatly talk to one another.  Here's more from Seth Godin's post:

"… is about making connections, about serendipity and about the network taking initiative.

Some deliberately provocative examples:

I'm typing an email to someone, and we're brainstorming about doing a business development deal with Apple. A little window pops up and lets me know that David over in our Tucson office is already having a similar conversation with Apple and perhaps we should coordinate.

I'm booked on a flight from Toledo to Seattle. It's cancelled. My phone knows that I'm on the flight, knows that it's cancelled and knows what flights I should consider instead. It uses semantic data but it also has permission to interrupt me and tell me about it. Much more important, it knows what my colleagues are doing in response to this event and tells me. 'Follow me' gets a lot easier.

Google watches what I search. It watches what other people like me search. Every day, it shows me things I ought to be searching for that I'm not. And it introduces me to people who are searching for what I'm searching for.

Seth Godin calls this Web 4.0, but as far as I'm concerned, it could also be called Web 2.0 or Web 3.0 - no one really knows for sure.   Another example - just along the last example I quoted from Seth Godin is this one from Going.com from TechCrunch - Going.com Gets Extra Social On Events:

"…Central to Going.com 3.0 is a new events and people recommendation engine that allows users to discover events and people in their area. The new features takes Going.com’s event focused social networking service to nearly a dating service. Where as before Going.com recommended events and tied together friends, the new version recommends new friends based on a users event history. Essentially it’s pattern based matching combined with Going.com’s event engine. For example if you’ve been to three or more events in the one city, and someone else has as well, they may recommend that person as a friend match.

I suppose you can say Facebook is Web 2.0 in that you can install applications that interact with your profile - but I might be stretching it a little. 

Anyway, that's my definition of Web 2.0, as much as I understand what it is, anymore than anyone else does.