For music, you can always use some "Google Hacking". Not quite sure on the legality of this...
Search using a string like one of these:
-inurl:htm -inurl:html intitle:"index of" mp3 "ARTIST/TITLE/ALBUM"
- intitle:index.of + mp3 + "ARTIST/TITLE/ALBUM" -html -htm -php -asp -txt -pls
Other than that, generally BitTorrent is very safe to use if you can get an invite to a "private" tracker.
If you're using Limewire, etc., either do not share files at all, or share very few. Generally, lawsuits target the uploaders. With p2p apps such as Limewire though, you have to be very careful. Make sure that the file size actually corresponds to the type of file (e.g. a songs should be about 5,000 kB). Viruses run wild on these networks if you're not "smart" about you're downloading. I heard a story that some guy was trying to download a song, but it was actually child porn, and he got busted, and is now facing a very very long prison sentence. Ouch.
I've also heard that if you have wireless and it is unsecured, in a lawsuit you could make the argument that anyone could have been on your network downloading it, but I have no idea if that would actually hold up.