Mega Man 2 and 3 both have some incredible scores that still hold up almost 20 years later. You can hear that amongst other things, the composer was definitely working the limitations of the NES to his advantage. I sometimes replay those games simply to listen to the scores while playing.
Kingdom Hearts 1 and 2 - especially 2 - each had this strange, almost hypnotic j-popish song that actually worked in their openings.
"Liberi Fatali" (FF VIII) is of course a complete must to talk about. Really. I only mention it this late because I didn't want to start off with an FF theme. Oh, and the score at the 2nd credit list in same game is equally awesome.
The opera part of "Moon over the Castle" which you will find in the opening of Gran Turismo 4... This is what opera is really about: To make some amazingly strong emotions in order to supplement a great visual element.