Ghosts 'n' Goblins (Wii, PSP, Genesis, SNES)
It doesn't matter which version you play - the arcade original, the Genesis' Ghouls 'n' Ghosts or PSP's Ultimate Ghosts 'n' Goblins - they are all ridiculously hard. Sometimes, yes, the game cheats, for instance by having gaps in platforms that you can't see, resulting in a frustrating death. But 90% of the time, you died because you didn't play well enough. It's heartbreaking to spend ten minutes inching your way forward, only to touch an enemy and fall into a pit, or be swept away by a tsunami. The jumping mechanic especially is incredibly unforgiving. Once you've chosen your direction, you only have one chance to correct yourself with a second, mid-air jump - otherwise you just have to sit and wait for the bones to clatter to the ground and that skull to slip, opening its mouth, as if to day "dammit" yet again.
And so, you play, you learn, you knuckle down. And the rewards are there. Massive, good-looking bosses (for their time) and the knowledge that you really accomplished something every time you clear a level. Try downloading it from Wii's Virtual Console. How long can you actually last without dying once? Hardcore games don't necessarily have to be majorly difficult, but in this case, it's the difficulty that defines it. G'n'G is a monster challenge. But totally, irrefutably worth it.