Pheonix and Frogger were I think the first real music-endowed games.
Classic-wise, my favorites are Gyruss, Moon Patrol, Pooyan (probably the most sophisticated original music of the period), Marble Madness (barely a Classic) - and, not mentioned yet, Xevious. Most of these were in '82, hence contenders, though Xevious is perhaps the quintessential music game, because it's barely music, and yet no diatonically lame.
OH, and Gunsmoke, which was '84!
Mid-to-late 80s: Outrun, Black Tiger, Indy, 1943....what else.......
90s, mmmmmm, Strikers1945 stands out.
@Vigo: dude, is that a chorus of gnats farting music?......
@lilshawn: well, not really. That basic minor key 'hey it's a tragic adventure coming' kind of thing (I think both Raiden and Twin Cobra have it), that...sad as *---fudgesicle---* to say.....is the common harmonic deal in all the kiddie metal in the last ten years....and has no sign of giving up. BLECH.