In September 2007, Universal Music Group (UMG) filed a lawsuit against the video sharing site Veoh for hosting videos that contained music the record company owns. The suit eventually had a part in Veoh filing for bankruptcy and selling its assets to another company. But in the end, Universal lost the original suit and the appeal — and it's all thanks to the Digital Millenium Copyright Act. Although the DMCA is often viewed as a tool of oppression, it has "safe harbor" provisions that protect hosting sites from liability for user-uploaded content that violates copyrights — but that could all change with SOPA.
According to the California court of appeals, sites like Veoh that make user-uploaded files publicly available are only required to remove infringing content when they become aware of the offending item, either by DMCA notice or otherwise. As long as the host diligently removes the violations it specifically knows about, it stays within the protection of the DMCA, even if it knows there is probably other infringing content hiding somewhere on the site. So next time your favorite video gets removed from YouTube, just remember that's precisely the action that protects the site from a full-blown lawsuit.