Ridge Racer on the PS1, trying to beat the black lamborghini. I was so fucking good at that game (or at least I thought so) that I could ace every course with perfect slides. It took me about 4 non-stop hours of playing to beat that one race, one tiny mistake even on the last turn and it was all over.
Karateka on the C64 was also notorious for making my friends and I cuss up a storm. One life to complete the entire game, you die and you start over from the first step. So many times we would get to the last boss and die, usually from that fucking bird. The game pace was so slow, it played at like 1 frame per second, and it took 3 - 4 frames for every input to register, so you couldn't stop once started a kick or something like that.