Pretty much the current generation of the internet and this will probably last til about 2012. It is the internet where blogging, social networking, forums, wikis, video sharing, webcams, sharing, getting pwned, etc. takes place.
Web 1.0 was the primitive internet where you went to campbells soup.com and there it is. Web 2.0 is pretty much where you can read and post blogs about soup and share info about your favorite soup on your Facebook profile. There is a Web 3.0 coming into the future which will probably be the iPhone Web, in which the internet might be in different places than a computer.
Kraft.com is Web 1.0
MySpace.com is Web 2.0