BitTorrent is a file sharing protocol. It (like other protocols) uses cleverly the bandwidth of many users (that belong to what is called a "swarm") to deliver some data to everyone that is interested. Everyone is supposed to upload data to other users while downloading, thus reducing the costs for anyone that wants to distribute a large file to many users. To join a swarm and download the shared file, you will need to download a BitTorrent client.
μTorrent is surely one of the most compact, stable and easy-to-use BitTorrent clients. But on December the 7th, 2006, μTorrent was purchased by BitTorrent inc. I was always a bit concerned about how good μTorrent was at protecting my privacy since it was closed source. But now I am not sure if I can anymore trust a closed source program that is owned by a company that is doing business with many "entertainment" media companies like Warner Bros and MTV. These companies will do anything to protect their millions and they wouldn't hesitate to spy on everything, so why not on the BitTorrent network?
I used Azureus for some time but I never liked it for the same reasons I do not like Java (which Azureus is written in): it is toooooo heavy. It needs some time to get started and then uses too much RAM. In addition to these, Azureus is not made to be portable. So although Azureus is a well-made open source application, I don't think I'll use it anymore.
What is left then? Taking into consideration that I am using Ubuntu and that I do not have any intentions to reinstall Windows in the near future I don't think that there are any good BitTorrent clients left. So, maybe I will continue using aMule: a program that connects to the great eDonkey and Kad networks and offers great variety of files while having nice mechanisms to reduce leeching.
EDIT: I now use Deluge on Ubuntu. :-)