There seems to be a consenous(ish) among players of Super Meat Boy (a mario-like, very hard, platformer) that using a controller is slightly easier.

Certainly I have tried playing street fighter with a keyboard and found it extremely hard.

Also, I couldn't imagine how you would play a 2d platformer which used an analogue stick. You lose the analogue if you map to the keyboard, and it doesn't really map easily to a mouse (as you can't keep moving your mouse in one direction forever).