YouTube hasn’t been completely left alone by the entertainment industry, a quick search on Google will show that they’ve had at least a couple of lawsuits come their way.
On the other hand, I think the length limit is probably the biggest thing keeping them from getting slapped with a major lawsuit from the major hollywood studios. They’re still so worried about people downloading full movies through P2P software in the days before (and right after) the movie is released in the theater that they probably don’t have a lot of time to think about YouTube users posting 3 minute clips of the movie, especially when they can just send a copyright notice and have the movie removed (though they have to keep doing it over and over again).
There are still a lot of protections in place for sites like YouTube, but in the end they’re still subject to some judge deciding there’s no legitimate use for their site and shutting them down. I think the movie and TV industries are still trying to figure out if a move to make that happen would backfire on them the way shutting Napster down backfired on the music industry.