I have tons of pet favorites, here are a few soundtracks that come to mind:
720 (Atari Games, arcade) - Totally kickass skate-punk soundtrack, which despite the huge "boom box" marquee and speakers was too hard to hear well in most arcades. It was released on a (strangely) Japan-only album called "That's Atari Music!," which is very hard to find. I had a rip of it briefly but lost it in a hard drive crash a while back.
Point Blank/Gunbullet (Namco, arc/psx) - I just think most people ignored the music in this one because it was a light gun game. It's really too bad, since its soundtrack is on-par with other new-era Namco games (Drill Land, Katamari, Outfoxies) in terms of totally bizarre and eclectic awesomeness.
Mario Party 1 - Again, to most people the music in a game like Mario Party is probably the least important and least memorable thing. It really rocks, though. The only way I can get people to even consider checking it out is by telling them that Yasunori Mitsuda composed it, which I don't think most people realized.
Poy Poy 2 (Konami, psx) - The more I bring this one up, the more I believe I'm the only person alive who has actually played it. That said, the music is fucking rad, though none of you will ever hear it. That is, unless I do a game rip, which I won't be able to post a link to for fear of being banned.
As for specific songs that might have been overlooked or possibly never even heard by a lot of people, which I think was the whole point of this thread, two of my big ones are from Um Jammer Lammy - specifically the songs "Treasure" and "Keep Your Head Up." Neither are actual level songs. Treasure is the song that you get to hear a few bars of as a parade of pregnant women parade down the street, and Keep Your Head Up is the ending credits theme. Both rule, though neither seems to stick in the minds of people who have played the game. Not even big fans of the game.
Another big one was the sort of hip-hop tune that plays in an endless loop in the background of the c64 breakdancing classic "Break Street." I haven't played the game since I was 5 or 6, but I still catch myself singing the tune practically daily. The bass line hooked me for LIFE!