I really like the reputation and collaboration pieces of this site.
What about creating a hosted service similar to ning.com and friends? Let users create their own communities, support it with Google-style ads, etc. You'd need a place to upload files, too, and include them in wiki pages.
I participate heavily in the Yahoo! groups list for a piece of enterprise software (Epicor Vantage). If there were a viable, and better, alternative to Yahoo! groups, I'd switch.
This idea feels like it's moving away from the core of what the SO engine is good at: Q&A. By the time you've added messaging, file uploads, wikis for everyone etc you'll end up with something more like SharePoint. SO is focused on Q&A - that's its whole purpose for existing: it helps people get answers to questions fast. To my mind, that's the only really important thing. The fact that it's fun and that eventually you get to know other users a bit is more of a means to that end than an end in itself.
I suspect it makes more sense for you to work out which bits of the SO stack you particularly like, and request those features in a site which is already aimed at social networking.
Maybe if Jeff & Co. decide to release an open-source version of the StackExchange framework someone could branch it out to accomplish more of the functionality you would expect in a social network or a Yahoo! Groups style site, but I wouldn't want to see StackOverflow itself (and it's primary framework) get developed into something it is not supposed to be, or try to be all things to all people.
That is a recipe in disaster. It is much better to focus on a specific target and shoot for it than to try to "spray and pray" and hope to hit every target imaginable.
I'd like to be able to add users to a "favorites" or "friends" list, and would also like to be able to private-message users directly through the site.
I say "yes" to a limited featureset.
