I am not sure about the whole Web 2.0 debate, but something which is very noticeable about the Internet in 2006 is that forum based sites are dying a slow death, and the sites that include a forum as part of their main site are doing even worse. Forums on those sites are being posted to less and less. It seems that much of the forum posting community has gravitated to either posting primarily on their own web blogs or commenting only on blogs. This has created a shift away from forums and for sponsored forums, it has meant a loss of ad revenue. It may be possible that this trend may continue and cause some sites to scale back or disappear completely.
Lack of Discussion
The most obvious turn off to forums is the moderator. Keeping the conversation going between multiple members is quite hard to do. Most moderators are faced with either not moderating at all discussions and letting other members get offended while a couple of members go at it and argue pointlessly about which operating system is the best or whether you support The President or not. Eventually moderators do buckle down and impose some civility and this causes hard core members to feel censored. Once they leave, the forum becomes a ghost forum with only old discussions left. A moderator is pretty much a thankless job.
Not Enough Ad Revenue
As for the webmaster, you have to pay for the forum software which is not exactly cheap or risk going with an open source script that will require more technical maintenance. Then you have to pay for the domain and hosting services; all of this is added cost. Most webmasters depend on some sort of steady revenue from sponsers and forums have a reputation for not performing well in this area, unlike blogs.
Ease of Publishing
The irony is that while forums were once the easy way to publish quickly, they are now being outclassed by blog scripts. Today almost anyone can learn to publish on Blogger or in WordPress, but learning to navigate, search, and setup your profile in most forums takes longer than the five minute WordPress install.
Then there is the obvious: web blogs have adapted the latest technologies like CSS, XHTML, AJAX, and other Internet buzzwords. Forums are just catching up and unlike small blog scripts, forum scripts are quite complicated and large, making even small changes sometimes requires thorough testing.
All of this leaves forums on the brink of unpopularity, forcing forum script developers to rethink their audience anf evolve into something else. Perhaps the web blog is the natural cousin to the forum, and the Internet may still have future uses for the once popular online forum.