Pirate Bay aside, pretty much all large torrent sites remove links to pirated content when they're asked to. Bitsnoop, for example, has deleted more than two million torrents, and at KickassTorrents the counter recently exceeded 850,000. Interestingly, Google often receives more takedown requests targeting torrents than the source sites themselves.
Source: TorrentFreak, for the latest info on copyright, file-sharing, torrent sites and ANONYMOUS VPN services.