I don't know about Super Mario 64, but when I played Super Smash Brothers Brawl using Dolphin on my PC I used an XBox 360 controller and it worked like a charm. There are adapters that allow you to use the original Gamecube controller on the PC too; and I think there are some Gamecube-like unlicensed controllers too.
edit: Same goes for Nintendo 64 controllers, AFAIK