I was just going to do a huge dump but I'll come back with various games when I find time later tonight. Got carried away with Xenogears, and probably would have got carried away with any of the OSTs I have on my hard drive.
Dazil (City of Burning Sands): http://www.youtube.com/watch?v=f2384v71q1g This song just seemed way too intricate for a video game at the time. It really felt like your character was in this strange new world and wasn't sure how to get out of his predicament.
Emotions: http://www.youtube.com/watch?v=_kZZvU0gWtY As far as world map music I don't think it gets much better than this, Mitsuda always excelled at making music you'd have to hear for hours and hours but wouldn't mind.
Light from the Netherworld: http://www.youtube.com/watch?v=FhGLbYe-oDU Opening credits theme. This was like the first video game where I really felt like I was firing up some kind of Hollywood blockbuster. The anime cutscene definitely helped.
Stage of Death: http://www.youtube.com/watch?v=bKMhA_imn1s And this was just the BASIC battle music, lol. Xenogears was awesome at making fights feel like life or death. I could have gone with the generic mech fighting music, but I always hated burning fuel in that game so I it leaves a bad taste in my mouth haha.
The One Who Is Torn Apart: http://www.youtube.com/watch?v=-_nr-Tj4dtU I'll just differ to the Youtube comment because it's hilariously over the top, but definitely captures how I feel about this and a few other tracks on this soundtrack: ...just a song...of one of the best OSTs and games ever made. For those who haven't played this game this is just a song. For those who have, this is a treasure that cannot be stolen.
My Village Is Number One: http://www.youtube.com/watch?v=k8_eAiO3kIE Not only an awesome title, but it was a real bummer when you realized you'd never get to hear this music again in the game.
Bonds of Sea and Fire: http://www.youtube.com/watch?v=hT5qYTlgLnk This was either more world music or the theme on Bart's ship, I think the latter. One of those songs you could just leave the game running and let soundtrack your day for a while.
One Who Bears Fangs at God: http://www.youtube.com/watch?v=19swM5L7_UQ I mean, the title says it all, right? I'm not sure there's a more satisfying final boss theme out there given what's at stake during the fight and all that led up to it.