Judging by this thread, I think many people will be surprised when I say; I cannot fathom how people can play with a controller, really. I used to play this game called Way of the Ninja, which is very similar to SMB but slower paced. From my experience with that I just use the keyboard, BUT, I had to change the keybindings. Space is simply too big of a button to push when it comes to this game, so I use A for sprinting and S for jump.
No problems whatsoever, my hands never hurt, finished light world and currently in hell with dark world.
So as I said earlier, I can't imagine how people manage to play with with a controller, I just can't. I tried it for a bit, but for me it's just too hard to accurately hit platforms correctly...
All in all, I just want to stress that it doesn't matter what you use, I see people here saying things similar to "I know I deserve to die because I use keyboard" and I say hell no! Use what you are comfortable with. The same goes to keyboard users, I don't understand why people use the controller, but that doesn't mean I don't respect you for doing it.
EDIT: In hindsight, it looks like I'm trying to brag when I state how far I've gotten, I'm not. Just meant to show that I'm progressing steadily