Apple has never been too keen on BitTorrent clients, blocking every single one from ever reaching the App Store. But even if you don't want to jailbreak your phone, there's a way around this restriction, and best of all, it's totally free!
Torrents, the bane of many a record and movie industry boss. While the download technology does have its legitimate uses, it's hard to argue against the fact that the vast majority of torrents flying around the Internet are of the less-than-legal variety.
Torrentula is a BitTorrent client for iPhone and iPod Touch which allows you to search and download torrents directly on your phone from some of the top Torrent trackers such as TPB (The Pirate Bay), Mininova, ExtremeNova, Demonoid, SeeQPod and SUMOTorrent. Torrentula can be downloaded from Cydia for free. You will need to first jailbreak your iPhone before you can install it.