mIRC - Some say this is the best GUI client in existance. If GUI clients are your thing, or if you are a beginner, this is probably your best choice. It's shareware of course. (Windows 95/98/NT, Windows3.x)

Pirch - This client has a lot of support as well, though not nearly as much as mIRC. Consider this as an alternative if mIRC just doesn't do it for you. (Windows 95/98/NT)

Ircle - If you use a Macintosh then Ircle is probably your best choice. (Macintosh, obviously)

BitchX - If you run linux or any of the various UNIX Operating Systems, I suggest downloading the source to BitchX right this instant. BitchX rocks. (linux, *BSD, etc)