Some of you might be familiar with flashget. Its the coolest download manager every to be created. Recently they have added torrent support also and now Flashget is irresistible. I myself am a flashget user for the last 10 years.
Its the most popular torrent client. It is very small in size (~1mb) and has got all the necessary features. Recently utorrent released their webUI using which users can control their torrent downloads remotely. Its a very cool application and Id suggest that you give this a try before you decide upon your torrent client.
A popular tool that has a built-in torrent search engine…you may never need to use a torrent search web site ever again with this product. BitLord is also very light weight. Whenever you download using bitlord, other applications might feel a shortage of bandwidth.
Azureus is a java based client and hence it works fine on both Linux and Windows. Its the most extensive Torrent client available and you need to be a real expert to take full advantage of its features. Its a bit heavy to operate and takes time to load or close.
If you are on Linux, I recommend the clients KTorrent and Deluge.