Super Mario 64 - Try to get on top of the castle, WITHOUT using the cannon (apparently it IS possible to do).
Super Mario Sunshine - Exactly the same thing, but on the Shine Gate instead (again, apparently it IS possible to do).
SMRPG: Beat Culex, without any of your party members dying.
And for a joke challenge:
Mario Kart Wii - Do an entire 150cc course with 11 CPU's, without getting hit by a Blue Shell/Bullet Bill (not even once).