I think the majority of music that Square use in their games is of the highest quality (minus the chocobo theme tune of course! ), from the early FF's, Chrono Trigger and Secret of Mana to their more recent titles; the music that plays to celebrate the end of each year in Final Fantasy:Crystal Chronicles is beautiful.
Metroid games for me also stand out in the music sense, not for their toe tapping quality but for the added feel of isolation that they add to the games from the original on the NES to the most resent GC outing.
Mario of course with it's world famous tune and two note sound effect that is instantly recognisable.
The Zelda's - like Square games, consistently excellent.
Castlevania: Symphony of the Night, the Waltz in that game is stunning.
Sonic the Hedgehog
Body Harvest - first game I played where I remember the music changing with the game play, from quiet soothing melody for when you where driving over the games land which would change dramatically whenever enemies approached.