Head to head to head to head: Torrent Droid, Torrent-fu, Transdroid, and BarTor. This isn't a full-blown review of any of these apps; just a quick demonstration to see which ones are worth your time. Here's a hint: save your money and go for the freebies.
The hardest part of using these apps is getting the settings right - like port forwarding. Someone aligned with Torrent Droid has provided a great wiki, which includes setting up a free domain for your IP with no-ip.com (i.e., username.redirectme.net). The Torrent Droid's home site, Zerofate, is down at the time of this writing. Looks like their service is basically dead as well. Well, Alec Holmes, thanks for starting something great.