Devil May Cry 3 - The final boss fight. I was getting my ass handed to me, but each time I retried, I kept getting better, until after the 20th or so time, I finally got the better of Vergil.
Mega Man & Bass - Again, the final boss fight. It's pretty far up there, with MM7's final boss fight. Many moments of "AAAARRRGGGGHHH! WHY MUST I SUCK SO MUCH!" followed by "HAHAHAHAHA VICTORY IS MINE, EAT IT *****!"
Starcraft 2 - Playing multiplayer 2v2 matches with a friend. Good times. Also, there was this one match I had (Zerg vs Zerg) where my opponent managed to sneak some Roaches into my base and wreak some havoc while I assaulted his base with a swarm of Brood Lords. After a tug of war of aggressive base expansion and placing a few Overseers in key areas, I managed to get the better of my opponent with a good ol' war of attirition.
Super Smash Bros. Brawl - I'm pretty much "that guy" among my friends when it comes to Brawl. I was playing Brawl with some friends, and there was also another "that guy." So we decided to have a 1v1 match on Battlefield (1 stock). I was Captain Falcon, and he was Sheik. After a fairly close battle in which my damage was past 100%, I managed to intercept him as he got knocked off the stage and tried to jump back on..... with a well-placed Falcon Knee.