It's a complicated question that is still being settled in court. The question is further complicated by which county you live in. Basically, if you share copyrighted material, you're breaking the law, and in countries where there are laws addressing this, you can be prosecuted. In the USA, the RIAA is focusing on ISP's and people with huge libraries of music and movies that can be accesses via P2P. Even Apple Computer finally went after a Torrent site that was hosting copies of its Tiger OSX.

The best protection is not to share copyrighted material, which means most music and movie files. The next best protection is live in a country where the RIAA or its local equivalents are prevented by law from gaining access to information about the location of your computer from the ISP it's connected to.

Purchasing the music or movies you've downloaded via P2P isn't any protection if you're sharing the files. The legal issue here isn't your right to make archival copies of your legally purchased music to play on your computer or MP3 player--the issue is sharing those files with people who haven't bought it.

I fear I may be digressing from your main point, though: If you can connect via P2P to download music from others and they can do the same to download from you, then you can't hide from the RIAA's seachbots. They know your computer's on the network, even if they may not know specifically who you are or cannot, for whatever reason, compel your ISP to disclose your name or location.