That old arcade gem, Black Tiger, AKA Black Dragon. It has these dragons that you have to fight, and I can't get past the 5th dragon, no matter how many times I play through. Damn some of those old arcade games were difficult, money-eating nightmares... even with unlimited credits I can't do it.
The very last boss in Alundra on the PSX is pretty damn tricky as well, that whole game is tricky, but still brilliant.
That big fat thing in Binding of Isaac is a bit of a nightmare as well, it just sits there while it's minions fire at you, occasionally firing - it's the sheer length of time it takes to kill, and the regenerating minions that make it difficult.
On console games though, I don't really have any memories of trully difficult boss kills, maybe I need to get myself Dark Souls or something really challenging like that. My character in Skyrim is so epic that nobody really puts up much of a fight, hehe, I remember I used to fear the dragons, giants and Deidra dudes. I guess the bears in Red Dead Redemption can be a challenge, sometimes at least, when your not expecting them.