Space Quarks
The Last Ninja
The original Pitfall
Rad Warrior
Teenage Mutant Ninja Turtles LCD game
Japanese Super Mario Bros. 2

These are games where you had to be right on the money every time or you would be seriously dead.

I think the hardest game I have ever played is Rad Warrior for Apple II. The farthest I could get was a meager appearance on the second stage of the radioactive jungle, and then I would die. It was hard as crap to get the anti-gravity suit in the first place, because you had to make an almost impossible jump, but then there would be another almost impossible jump followed by missles and apes picking their nose and trying to put radioactive snot on you.