Some of my favorites are:
The first battle with Magus in Chrono Trigger is something I'll hold close to my heart for the rest of my days. The buildup, the dialogue, the environment, the music theme, and the battle.
"Magus risks casting a spell"

Omega Pirate in Metroid Prime really got my blood pumping. I was
seriously into that.
The Werewolf in Castlevania Chronicles. Some people hate that fight, but I think it is intense and awesome. I also don't think it's cheap. You just have to know how to win, but it can be very difficult.
I also really like the Dracula fight in Dracula XX.
There are many others, and I'm not even sure if the above are my favorites.
EDIT:
Oh, I know another one. The battle with Wiegraf/Velius in Final Fantasy Tactics. Classic moment. Chapter 3 of that game was loaded with awesomeness. I actually like the Orbonne Monastery battles with Izlude and Wiegraf more, but I'm not sure if those would be classified as boss fights.