It depends what I'm after,
BitTorrent:
uTorrent is extremely light weight, very versatile and I'd recommend it in an instant. Very good for people who just like to download stuff.
Azureus is pretty hungry for resources, but it's by design (because it exists for so many platforms it uses Java and the like and it's a pig to be kind) but it's extremely powerful.. it has a plugin system with some excellent features such as a status emailer that will send you an email when a download finishes (good if you have email on the phone), and a web interface so you can control it from another PC/XBOX/Similar (uTorrent has a webui as well now).
For everything else I use LimeWire, it's got it's share of fake stuff like everything but of the programs I've tried it's the most useful at finding good stuff. Be weary, it also uses Java and is also a pig.
EDIT: Just looked up the program patriot mentioned, looks much better than LimeWire so I think I'm going to start using that - good call mate