I've been listening to video game music a ton recently, so I suppose I'll contribute to this.
Choosing the top 5 soundtracks for all videogames is pretty much impossible for me, so I'll limit places to one per series (or composer, even). Actually, since it's only 5, I'll also try to list what other people will probably miss. I won't order them, either, that's another impossible task...
Heroes of Might and Magic III:
The Heroes series has amazing music. If you haven't played or heard of these games, do look into it (now!), especially if you're a fan of turn based games. I see many people at VGC seem to play either primarily Japanese games, or Console games. These people need to give Heroes a shot, you won't regret it! I'm considering making a thread later, just for this purpose...
Fav tracks: Combat 2, Rampart Town, Stronghold Town, Rough
Warcraft II - Tides of Darkness:
Something about the older game music really gets to me. Warcraft II's soundtrack really nails the feeling of war, just give it a listen. It has so much oomph in it, it's ridiculous. This is the start of Blizzard's dominance for ya.
Fav tracks: Human 2, Orc 3
Phoenix Wright Series (T&T beng the fav):
These games would not have worked nearly as well without the amazing music. T&T music was done by the composer of Grandia (which has been given 3 mentions in the thread already, surprisingly). He's done the Miles Edgeworth game as well, can't wait for it to come stateside.
Fav tracks: Objection, Cornered, Announce the Truth (from JFA, just had to include this)
Jet Set Radio:
What would this game be without its crazy soundtrack?
Fav tracks: Humming the Bassline, Funky Radio, Let Mom Sleep, Mischievous Boy
Mega Man 2:
He ain't called "Rockman" in Japan for nothin! Easily some of the best music on the NES in this game.
Fav Tracks: Metal Man, Quick Man, Wily 1, Air Man, Bubble Man, Flash Man
Well, that's 5. Too small of a limit for me to be satisfied with my list! Of course, since I also love all of the obvious choices (FFs, Zeldas, Chrono Trigger, etc), I just let others list them for me.