cliche points: ff4 thru 6, but particularly the 5 intro and various from 6, which even made it to my phone playlist (terra/overworld, w.o.r. airship, opera...). there's a couple-a-three from 7/8/9 that are quite nice, but i just don't "get" them as much on the whole; the snes ones seem to hang together as a coherent soundtrack a lot better. and there's the whole eyes on me nonsense spoiling it.
can we toss in the xenogears theme to that pile? I can't remember if that was a Square release.
gran turismo (from 3 onwards), GTA and tony hawks series in general
now i'm reminded of it, Doom was pretty good, yeah. As well as Descent. OH! And monkey island 1 & 2 to boot. They all used the unique sound of the old soundblaster OPL2/3 synth chips to their full potential, rather than simply chucking some general midi stuff at them and having mutilated crap come back. MI2 had the adaptive sound too, of course.
MGS, duh. Almost all just atmospheric but damn good with it.
Worms, ditto. But it had an actual theme song too!
Forgotten gem: Tempest 2000. Either in soundblaster synth OR CDDA form. I think I actually taped the CD version at one point and used it as beach reading/thinking/working stuff out vs snoozing-time coordinating music.
Not actually too many I can point at from my truly early gaming days, but Sonic and Streets of Rage on the gamegear were pretty good, considering it was an also-ran 8 bit handheld. Supercars and IK+ on the ST of course (even though the latter only had one theme, it had an unheard-of something-like 7-8 minute loop length) plus Speedball, Xenon, Turrican, and a few coverdisk games which no-one will ever have heard of. All created a unique "sound" for themselves, which is a hell of a feat on a 3 squarewave + noise + envelope machine.
But none of them can beat the humble speccy, whose every game came on an audio cassette that could quite easily double for ten minutes of highly experimental industrial breakbeat electronica screamcore that aphex twin would be proud of.