If you had any doubts, the New Scientist has published a report that says that most torrent downloaders have their internet protocol ("IP") addresses logged within three hours of the download.

The article wonders whether the information will be reliable enough to be admitted in a court of law, but another legitimate question is whether there are many who can afford to fight the evidentiary battles. The owners of copyrighted content are very good at targeting the price points where it is cheaper to settle than to fight.
BitTorrent is seen as a godsend to many illegal downloaders, but it should be seen for what it is: a trap. To participate in a "swarm," you have to give up your IP address, so that the other members of the swarm can copy from and to you. If you don't want to leave your home address with the owners of the content, then do not use BitTorrent. The End. Finis. Owari.