Hmm...for me, it was a combination of four somewhat older games; Jak and Daxter: the Precursor Legacy, Jak II (two games that are part of an awesome four-part series that NO ONE seems to remember), Kingdom Hearts and Chrono Trigger.
For the first Jak game, it was mostly the ending that had me riled. You mean to tell me that I spent all this time defeating Gol and Mia for one last lousy COLLECTION QUEST!?!? SCREW THAT! (Of course, I did it anyway, but it still pissed me off)
In Jak II it was the mission with the yellow HellCat Cruisers. That took me FOREVER to beat! And that was before there were difficulty levels! There was only one, and it kind of varied between 'cozy Sunday stroll' and 'ASSRAPE, NO LUBE'.
Kingdom Hearts mainly annoyed me because it would always ramp the difficulty to insane heights early on in the game...normally in the Deep Jungle and Wonderland levels. (I swear if I have to die with that invisible iguana one more time...)
Finally, there was Chrono Trigger. Mainly for the Lavos fight. Now, this wasn't out of constantly losing. In fact, I was so elated, relieved, excited, and yet exhausted when I beat it on the first try. No, this was mostly out of my sheer frustration of fighting three bosses at once, one of them actually being composed of all the other major bosses I have fought thus far. MAN, was that such a pain in the ass!
Oh yeah, and that final boss fight with Jack at the end of the original pre-Lost Chapters Fable, during my first run through. Those of you who remember your first playthroughs of that game know what I'm talking about. For me, that was mostly a battle of attrition...spanning three hours.