I sometimes spend 14 hours a day working behind a PC. Any action that requires me to push the rodent around annoys the crap out of me.
So I’ve ditched the mouse and gone with a Wacom pen for the times that I can’t avoid it.
I also use Ratpoison as a window manager, so I can perform basic UI operations without resorting to the rodent. Also, Ratpoison doesn’t clutter up my interface with useless crap like “window decorations”, “window buttons” or “interface themes”. I don’t like them, I don’t use them and I really have a better use for my screen real-estate.
Because I do a lot of web development stuff, I use the Firefox plugin Conkeror most of the time.
I email with mutt, read feeds with snownews, edit anything non-binary with VIM, edit binaries with BIEW, read Usenet with tin, watch movies (on a remotely controlled display) with mplayer, I play music with mp3blaster and manage my ipod with gnupod.
For experiments with alternative inputs that do require pointing devices, I’m interesting in Dasher, which you really should check out if this is your kind of thing.