The DMCA lets copyright holders send takedown messages to various sites, demanding allegedly infringing content be taken offline.
It's been rather successful in doing that. A few years ago, a great site, Chilling Effects sprung up to track all sorts of takedown notices (not just having to do with copyright, but any kind of cease & desist threats -- though DMCA takedowns are common).
It's a joint effort by the EFF and a bunch of universities, and has been...