I'm predominantly left-handed, except on the computer. Where I use the mouse with my right hand and play FPS games using the mouse on my right hand, as well. Not sure how common this is.
I do think I'm more accurate with my left too.
Before using WASD, I used WER and Space key for movement. Q=Jump, W=Forward, E=Strafe Left, R=Strafe Right. This allowed me to easily reach the number row and remap T=Chat 123456ASDFG for switching weapons and game controls. I switched to WASD with World of Warcraft, and use that for everything now mostly out of laziness and inertia (tired of rebinding everything, as you do).
I tried to use the mouse w/ my left hand and couldn't. Too much of the controls are right-hand centric. Keyboard shortcuts for browsing are all on the left side, etc. It does feel nicer to have it on the left hand sometimes.