Battletoads and Ninja Gaiden were the games I couldn't beat and still can't without a save state.
Another hard game was T.M.N.T. I did beat it but only a couple of times and took me about 2 years to master.
There are other games out there that were hard but the controls sucked so I blame that. Like that bart simpson game where the run button was also your jump button. Makes way more sense to make it a la mario with two buttons.
On the Caslevania II, I managed to beat that one only because other friends told me the 'secrets' on what to do.