Who owns your social media data?

Andy Baio, in writing about the shutdown on CNet geekster online dating site Consumating and the fact it had a strong little community going, whether it scaled up to thousands or not (millions, not for sure), asks “Since online communities are built on top of user’s contributions and social interactions, it raises the question: are companies responsible for keeping community website alive, even after they cease to be strategically desirable?”
This is a great question and hits a grey area many community or UGC web sites end up sitting in.
On one hand, if it is the users’ data, does that mean the site has an obligation to preserve the data for the creator (and make it exportable)?
On the other hand, if it is the site’s days doesn’t that both give away assets people might want to keep (like their words and photos) and potentially make the site liable for any copyright infringements or problems users of the environment incur?