Well, filesharing is very useful but I'm really more interested in the forum/wiki side of things - asking questions, getting answers, writing articles and commenting.. showing off your conquests... Pretty much exactly what we're doing with this bulletin board.
I love the forum format because it's so simple and free form.
Think about how it works in the most abstract terms: I login to the server and enter a post, text with a bit of formatting, nothing fancy at all.. It goes into a database. Other people login and read my posts, and post their replies.
Look at the contents of our posts. Is there anything at all in there that requires the complexity of HTML+CSS+JavaScript? It's wasted! A 128K Mac should be able to handle this! The only reason it requires a huge memory hog of browser is because the presentation of the data is tied to the Web and the technolgies the Web is built on.
A protocol for accessing and replying to posts in plain text or a simple rich text format - or even complicated rich text, with multimedia and what have you - on a remote server is trivial. You could have a web client for those that love the web, or you could have a real desktop app, all interfacing with the same servers, seamlessly.
You gain flexibility (choose the client you want), lose complexity by using existing functionality (think opening videos in QT Player instead of the browser plugin hell I'm sure we all remember), and you kill this horrible idea of making user interfaces with HTML+CSS instead of, you know, user interface toolkits...
I have to go to bed now. This is an idea that's been brewing for a while, and really, it's quite obviously superior to the web in every single way for communities like ours. I'll write more about it sometime soon.