Hm. Off the top of my head:
Ninja Gaiden/NG II
. The NES versions, that is. I don't recall ever getting past the third level in either game. Damn birds always hitting you in the middle of precarious leaps...
Super Mario Bros.: The Lost Levels
. Let's just say that there's a reason why, in Super Mario All-Stars,
the game would start you over at the beginning of each individual level after a Game Over, rather than the start of the world. There's a reason it's listed on TVTropes's Platform Hell
page, rather than their Nintendo Hard one. The first game with poisonous mushrooms, powerups that are otherwise rare enough that you'll spend the majority of your time one hit from death, new platforming elements, Warp Zones that force you to restart the entire game
...I could go on. This's probably the one I'd pick; even though I beat it, it took an ungodly number of tries.
on the PS2 for more recent games. It's a side-scrolling Action-RPG/Beat-'Em-Up that continues the tradition of Atlus releasing challenging games. Put simply, near the end of each character's story, even the regular enemies will be powerful enough to kill you in just a few hits unless you've done some massive power-levelling. Like, two or three hits in some cases. In fact, one area has enemies that one-hit-kill you if they explode on you, and another focuses largely on the annoyance factor--they hit you once, you're open to more attacks from all sides. Good thing pretty much everything else about the game rocks as well.