I consider the most sophisticated apps today to be web 2.5 ("service web"): cross-site APIs/widgets and the resulting mashups.
And then web 2.0 ("social web") as single sites with readable/writeable content. Forums, social news, sharing sites.
Web 1.5 ("application web") as writeable sites. Webmail, instant messaging, site builders, search engines.
Web 1.0 ("document web") as single sites with solely readable content. Blogs, arcades, galleries, oldnews, papers, homepages.
When we integrate structured portable data, the social graph, cross-device interfaces, and decentralized identity, I think we'll have something to call web 3.0.
Read about "Hype Cycles" if you are not already familiar with them: http://www.gartner.com/pages/story.php.id.8795.s.8.jsp
As i see it, the dot com bust (or web 1.0) was just the natural "trough of disillusionment" for the hype cycle of the Interweb.
Web 2.0 is just the "slope of enlightenment" for the aforementioned Interweb (now known as the Intertubes)
M.
(Yeah, I made that ...)