Quote from Cevlakohn:
I'm a softcore, and too high of a difficulty turns me off of a game rather quickly. That said, the hardest games I've played significantly (though not beaten) are Ikaruga and Super Monkey Ball on Expert mode.
Expert Extra 9 is probably the big stopper of getting to Master, but Master is where you will need those infinite continues, particularly Master 3 and, to a lesser extent, Master 9.
F-Zero series're pretty good about making the curve steep, but rewarding-
GX V.Hard story is tough, but I think doing all the Master cups on each machine is tougher.
(Incidentally, it's more fun to beat Deathborn without abusing his Rubberbanding, and freakishly difficult. Also, you can slightly exceed the countdown in the "Escape reactor" mission. The F-Zero Grand Prix stage and the "training" stage're probably the hardest in my opinion.) On the other hand, it probably has the easiest stages labeled "Fire Field" of any of (1, X, GX, MV).
Agree with 7th Saga.
Blast Corps, particularly the Pac-man-ish stages.
Kid Chameleon.
Honorable Mentions:
Megaman 1 for Fire Man & Yellow Demon (w/o slide)
Megaman 7, Wily's little pod with elemental attacks
Wario Ware's final story stage, for tending to kill me before reaching the final break more often than not, unlike any other
Rygar(NES)'s forest boss.
Melee enemies in the latter part of Faceball 2000.