NHLPA for the Sega. Not against the computer but against this friend of mine who's "nintendo thumb" is the size of my thigh but more sensitive than, er, you get the idea.

Ghosts N Goblins had fairly bad play control and really nasty enemies that could kill you in one or two hits. It was a very unforgiving game and the sequel for SNES was even worse.

Ninja Gaiden III. If Ninja Gaiden 1 was difficult (I frequently see it listed on "hardest games" lists) then part III must be too hard for Zeus to beat. It took me ages to beat Ninja Gaiden I, and then I mastered II fairly quickly - although overall I liked it the best. And then here came III. I was so excited. But they totally fucked up the control of Ryu and introduced all of this weird cyborg-techno crap and to make up for the somewhat easier part II, made the third or fourth level of the game as difficult as the last level in part one. It was nuts.

Ninja Gaiden for X-Box as well, although it pales in comparison to Ninja Gaiden III.

Transformers for NES. I can not get past the first regular enemy in the game. You blow something up, a little guy escapes and shoots your huge transformer with a tiny bullet and you die. Every time. I have no idea if it is even possible to get past that point, but the creators must be found... and slayed.
It isn't worth playing, just take my word for it.

TMNT for NES. WTF? That game seemed cool for the first few minutes but soon you realized it was the most tedious, insanely difficult game you had ever seen. Anyone make it to Shredder? It is like standing in hell fighting Satan with a match. Your turtle just looks stupid while Shredder bounces around and... shreds you.

I could name quite a few hard space shooters (Pulstar for Neo Geo being the worst, probably) but not that many people like them to begin with.

Mega Man. Parts of Mega Man 2. Horrible play control, yet addictive to play. Lots of annoying jumping in the first one which was really the hardest part of the game.

Blaster Master. I freely admit I never bothered trying to finish this one. I would make it to the last level and then have no clue what to do. Horribly hard.

Kid Icarus. Oh come on, you stupid little angel! *throws controller*

more later.

bionic commando for nes.

devil may cry was pretty hard.

The music from TMNT still haunts me.

People often mention Battletoads as being a particularly impossible game. I'm not an expert, though.

Super Magnetic Neo for the Sega DC is really trippy and absolutely hard with a no-fault-tolerence control scheme.

The best games are the ones that are really hard but worth it. Like F-Zero GX for the Cube and parts of both Metroid Prime games. Or the Tony Hawk games until you get the hang of them.

I thought Half-Life for the PS2 was relatively hard, and when it overwrote my save at a point where I was stuck on a box and couldn't escape, I just couldn't bring myself to start over.

A little part of me died that day.

OH, WAIT! Taiko Drum Master. UNBELIEVABLY hard. My neighbor across the street has been a professional drummer for years and complains all the time about how hard the devil setting is.

Supreme Warrior. Talk about lousy control settings.

There are a lot of different reasons why a game might be hard. Off the top of my head--tedium, like E.T. for the Atari 2600; memorization, like tournament-level fighting games; timing, like Taiko Drum Master; time commitment, like Animal Crossing. Oddly, many of these games are very easy in other respects--Taiko Drum Master, for example, is a very short game, and Animal Crossing is easy in every other way.

Dreamcast Powerstone II: you are Galuda, playing against 3 Chefs on the same team, difficulty level 8, on the Space Elevators map. One must make all the right moves to win, or the Chefs will fuck you up.