I used to have Azureus set up as a background daemon (i.e. running in the background with no visible user interface). I had the web interface plugin installed so I could manage it via a web page.
However, I never really got this to work particularly well. Azureus application and plugin updates went unnoticed and it was something of a pain. So, I've instead gone back to running Azureus in the usual fashion, but set to launch hidden. I still access it via the web plugin, since the html interface is much cleaner than the Java UI. Plus, it means I can tell my Mac Mini at home to download a torrent and can check on progress via the web interface from any other machine on the internet.
Azureus isn't too bad on CPU use, even with my G4 Mini. It's something of a RAM hog at times though. My mini's also running the Webmin web-based management interface. I've got a few custom commands in there that allows me to close and re-open Azureus remotely. This comes in handy if I'm streaming video from the Mac over the internet and need to close Azureus to free up some bandwidth.
As for what I use torrents for... well, pretty much anything that's of a significant size. Even Microsoft these days provide torrent links for some of their content (such as their trial software).