Jason just blogged his take on an official definition of "Web 3.0" -- in his case he defines it as better content, built using Web 2.0 technologies. There have been numerous responses already, but since I am one of the primary co-authors of the Wikipedia page on the term Web 3.0, I thought I should throw my hat in the ring here.
Web 3.0, in my opinion is best defined as the third-decade of the Web (2009 - 2019), during which time several key technologies will become widely used. Chief among them will be RDF and the technologies of the emerging Semantic Web. While Web 3.0 is not synonymous with the Semantic Web (there will be several other important technology shifts in that period), it will be largely characterized by semantics in general.
Web 3.0 is an era in which we will upgrade the back-end of the Web, after a decade of focus on the front-end (Web 2.0 has mainly been about AJAX, tagging, and other front-end user-experience innovations.) Web 3.0 is already starting to emerge in startups such as my own Radar Networks (our product is Twine) but will really become mainstream around 2009.
Why is defining Web 3.0 as a decade of time better than just about any other possible definition of the term? Well for one thing, it's a definition that can't easily be co-opted by any company or individual around some technology or product. It's also a completely unambiguous definition -- it refers to a particular time period and everything that happens in Web technology and business during that period. This would end the debate about what the term means and move it to something more useful to discuss: What technologies and trends will actually become important in the coming decade of the Web?
It's time to once again pull out my well-known graph of Web 3.0 to illustrate what I mean...
(Click the thumbnail for a larger, reusable version)
I've written fairly extensively on the subjects of defining Web 3.0 and the Semantic Web. Here are some links to get you started if you want to dig deeper:
The Semantic Web: From Hypertext to Hyperdata
The Meaning and Future of the Semantic Web
How the WebOS Evolves
Web 3.0 Roundup
Gartner is Wrong About Web 3.0
Beyond Keyword (And Natural Language) Search
Enriching the Connections of the Web: Making the Web Smarter
Next Step for the Web
Doing for Data What HTML Did for Documents