The Simpsons: Bart vs. The Space Mutants... I used a guide and even then, it was a nightmare, half the battle is knowing what to do, the other half is fighting the slippery movement.
Without a guide, Mega Man V. Not particularly hard, but for a 7-year-old beating it meant the world to me.
My current nemesis is Disney's TailSpin for NES, those patterns are really devilish.