There are many Bit Torrent clients out there which do offer some kind of privacy protection, but they are often offered through slow proxies or paid VPN services. Tribler takes a different route with its Tor-like Onion-style network which helps make your file sharing anonymous.
Tribler is a nice-looking application which has many useful filesharing features and it does most of what other, more popular torrent clients do. The interface left-hand panel provides access to its main features (search results, downloads, channels, etc.) while the larger panel on the right provides details about search results and downloads.