What was the hardest boss you ever fought in a game?

Ninja Gaiden 2 xbox360 version...almost 40 times...i hate this bug!

No where near as hard as some of these, or even some of the bosses in that game, but I remember being stuck for weeks on heroic Deathwing in WoW. My guild was 2nd Ally kill on my server, 4th overall I think, and we missed 1st Ally kill by roughly 5 minutes x) If we had just been 5 earlier, we would have had the 3rd kill on our server. Same with heroic Ragnaros. Spent weeks on it, burnt through recruits like a fiend, but that time we were 4th Ally kill I think? All I remember is is being so frustrated I couldn't even enjoy it when he finally did drop lol Those two bosses had me wanting to chew glass

Reach 500 seconds in Devil Daggers

That would be the Immortal One in Lost Odyssey.

Emerald Weapon in FF7 I think. I'm sure there are some others but this one comes to mind instantaneously.

Vergil from Devil May Cry 3...

I think it was the last boss of Star Fox Adventures. That wasn't hard, though ... it was plain bullshit.

Interesting question, today I decided to try and finish Touhou 6 Embodiment of Scarlet Devil with no continues. It took a number of tries but I eventually did it, and that allowed me to finally unlock the EXTRA stage.
Then I Itried the EXTRA stage and I got totally destroyed by the boss of the EXTRA stage. Bullet Hells in general probably has the hardest bosses I've faced.
Not sure what I'd say is the hardest boss I've also beaten, DMC3 M20 Vergil on Dante Must Die difficulty maybe?

Teenage Mutant Ninja Turtles
Whole game was one big boss for me and I failed to beat it %(

Wily in Mega Man 7, with a keyboard. Why oh why did I decide to use a keyboard for a Mega Man game? Did I not have a working one back then?
Wily was bullshit hard and had attacks that you basically never see a boss use in that franchise, because something so OP would be terrible to fight in a small area and took forever to kill. Bad game design.
He fires off several super fast orbs at once that either stun you for a few seconds or rip through your health. One of them locks you in place so his next attack will hit you and DoTs for like a quarter of your health. Only way to dodge is to mechanically jump over a low orb and slide so the others home right over you, within a second of appearing. Keyboard is not that fast to react with. He appears high in the air and disappears for a bit in case you try to hit him more than once.
He appears as the same boss in the sequel and is so toned down as to be a joke battle. Almost weak to Top Spin kind of joke battle. None of his old attacks make an appearance.