First thing that comes to mind is this:

Yoshi's Island - Final Boss (Baby Bowser) - This may not seem like much now, but at the time, it was a pretty neat way they changed the perspective of the last boss fight and the music was really awesome as well. Baby Bowser wasn't a terribly hard boss, but it could be tricky, especially when your footing kept getting destroyed and made it easy to fall off. Great finisher to an already great game.

Super Smash Bros. Melee Event 51: The Showdown - I loved this battle. At first, it was frustrating as hell, but eventually it was just too much fun pounding the stuffing out of Mewtwo, Ganondorf, and Giga Bowser again and again that I went ahead and beat it with every character (some were definitely harder than others, and I think Ice Climbers was where I had the most trouble). I found the best character to use for this battle was Fox, as Mewtwo and Ganondorf mindlessly wear out their shields if you just keep spamming laser fire at them and you can run circles around Giga Bowser with the help of Fox's jet pack as soon as he got close. Overall, it's a fun battle.