i see a couple people have answered, but:
NO, bit torrents are not illegal in any way. however, receiving/sharing copy-righted material with anyone, even if you own the material personally, is illegal.
That last part is not strictly true, depends on the word own.
If you own copyright to material, you own distribution rights and can torrent it.
If you buy a CD or DVD, you own a piece of plastic, but you don't own any distribution rights to the content, in which case, torrenting it is illegal.
If you have access to copyright material not your own, but publicly dispensed by the copyright holder as free to re-distribute, torrenting it is legal.
If you are using torrent downloads to gain access to things being sold, then you are trying to get something for nothing and ought have the common sense to know that's theft, and is illegal.
A car isn't illegal. Operating one without a license, tags, insurance or while under the influence, is illegal.
Torrent software - same thing.
OP, just say, how do you intend or want to use it? That's the crux of your question.
If for media piracy, be advised, laws are stricter and in addition to fines, you could face jail time, so it's not worth the risk.
And any site saying that they are not responsible if content is copyrighted is run by fools. Long before Megaupload, I documented here the first case of an operator getting a long term of hard time in a Federal penitentiary.
But for all of the legal uses, torrents are great.
Just like cars.