Blaster Master, which I'm ashamed to admit that I've never finished.
Street Fighter 2010, finished this a few times and have played it some again recently... still pretty hard but I got back to where I could consistently get to the 4th planet without too much trouble.
Castlevania 1, the hallway leading up to Death and then Death himself. Holy crap.
Ninja Gaiden 1, level 6-3 and all of its "why in Goku's name?!?" difficulty. There was a faq on gamefaqs just for 6-3, iirc.
Ninja Gaiden 2 I got fairly good at again last year, but all of level 7 still kicked my ass. Haha.
Edit: just remembered a few more.
Power Blade
Double Dragon series for NES (platforming elements and death pits in a beatemup?!?)
Mega Man 1
Gradius series
Super Aleste aka Space Megaforce (one of my favorites growing up but man it's tough)