Ninja Gaiden 2 on the NES. I want to finish it but I keep on dying in Stage 4 (and of course in all three stages before, too) and that's usually the point when I give up. Even though there are infinite continues, I still move on eventually.
A more recent game would be Alien Isolation, but that game is actually not difficult, but rather cheap. The goddamn Alien is purely randomized and no matter what you do, chances are the fucker still catches you eventually just because. That's bullshit.