BitTorrent downloading on mobile devices was first introduced on S60 devices with the app SymTorrent and now we also have bittorrent client for iPhone.
Torrentula is a free bittorrent client for iPhone and iPod Touch that allows you to search and download torrents directly from your devices. This app is available through Cydia which means you will need to have a jailbroken iPhone/iPod Touch.
In spite of big names in BitTorrent clients like uTorrent, I like to keep trying out new clients which may offer better speeds and features.
In another such search, I came across BitSpirit. It supports a number a personalized features and full BitTorrent protocol implementation. It is a powerful BitTorrent client with a clean and easy-to-use interface.