I run a UGC site on a dreamhost virtual private server called cueflash.com. A user posted up content that was copyrighted, and dreamhost recieved a DMCA takedown notice. They shut my site down, without first giving me any notice (though, in their defense, it was easy to turn it back on).
I also run a UGC site on linode (editthis.info), and had the same situtation there (except the person who made the complaint was wrong and I protected the users' contributions). Linode actually allowed me to address the issue rather than just pulling the plug.
If you are going to run a site where a user might post something that violates copyright (a forum, a blog with comments, or practically anything), and you would prefer not to have a provider that shoots first, and asks questions later, go with Linode. http://tinyurl.com/25x4bk5 (my referral code is in there)
Linode - Xen VPS Hosting