Mega Man vs. Bass, it's just the best damn thing ever to happen in that series.

I've definitely gotta agree about Psycho Mantis. They threw out the rule book on him. He's by far one of the most interesting fights over put into a game.

That boss from Gunstar Heroes who has 7 different modes (I think it's just Green's mech) is also amazing. Not terribly difficult, but incredibly cool and stylized.

I also love the first boss from Run Saber. I don't know if it even has a name, but the fact that you're basically having a lightsaber duel on top of a plane mid flight that does some minor aerial stunts makes it very memorable.