Most difficult game you've played for every system.

[Peter1986]

Nintendo --- "Ghost'n Goblins"
Yeah, you knew this one was gonna be mentioned.
It's not even the Red Devils that give me the most problems - I got used to their relatively predictable attacks patterns in the NES version some time ago, they are much more random in the arcade version - I have more problems with the two final stages, where the game basically decides to throw as much crap at you as possible.
Narrow hallways with Big Men, Red Devils and Forest Ghosts ganging up on you?
Yep, that's stage 5 and 6.

Super Nintendo --- "Space Megaforce"
This game is extremely brutal on the hardest difficulty - "Wild";
every enemy will disintegrate into deadly projectiles when you kill them, which can easily flood the entire screen, and there are so many enemies everywhere that you sometimes absolutely need to use a Bomb in order to realistically clear the screen - it's probably the closest that I have seen a regular space shooter come to something that resembles bullet hell, without actually being a bullet hell game in itself.
It's a GREAT shooter, though - definitely one of the very best space shooters on the whole system - and it's surprisingly unknown.

Nintendo 64 ---"Perfect Dark"
It seems like everyone has forgotten about this great FPS classic nowadays (at least the actual N64 version), but anyway, it's definitely one of the hardest games to beat to perfection.
There is no recovery time, so you could get killed in one second if you stand in the enemies' line of fire, and you always need to pay attention to everything that happens around you - the guards are also pretty smart sometimes, and will occasionally wait for you to come to them instead of chasing after you, which makes them more unpredictable.
Also, unlike its better known spiritual precursor "GoldenEye 007", you will have absolutely no hand-holding on the hardest difficulty;
in GoldenEye 007 you could sometimes find Body Armours lying around even on 00 Agent, but in Perfect Dark you will get no extra protection whatsoever on any stage if you choose to play on the hardest difficulty, Perfect Agent.