The sound Tracks to the Kingdom Hearts games have always blown me away. Their music is so soulful and unique. It's very marvelous.
I also very much enjoy the Music for Sonic the Hedgehog games. They've always done very well in giving me the "amped-up" feeling that goes so perfectly with fast paced games like that.
Pokemon game music has always been very good also (with the exception of some of the Black and White 2 stuffs like Hugh's theme and N's). My favorite of that group of games is the Ruby/Sapphire/Emerald musics. The use of the trumpets mixed with really intense drums and sounds really made me happy to play those games with the volume all the way up.
Well, in my humble opinion, the soundtracks for Legend of Zelda Games are just perfect. I - sadly - haven't got to play any Zelda game other than "A Link to The Past - that because of my lack of access to consoles/emulators to play them - however, I have watched many videos about Zelda games and, man... those soundtracks are awesomely perfect. Specially in the N64 title "Majora's Mask"
Additionally, The Elder Scrolls: Oblivion and The Elder Scrolls V: Skyrim have nice music as well. In TESV, those nord chants can make any warrior act viking-like and fight everyone to get to know more about the Dohvakiin stuff.
By the way, for people that enjoy metal and hard-electronic tunes in their game's soundtracks, I'd recommend Killing Floor's soundtrack. Those tracks - specially the boss battle song, called "Abandon" - can really deliver a violent atmosphere for fighting tons of zombies... er... "specimens".
I don't know if this counts but the car radios on gta vice city and san andreas were great.
I agree with Cale. GTA: VC's soundtrack can really establish the mighty "80's" feeling to the game, making every ride one of the most authentical, 80's experience. And GTA: SA's soundtrack reflects the atmosphere of the San Andreas state: K-Rose for countrymen/country style enthusiasts, K-DST/Radio X for rockers and Radio Los Santos for the fans of rap.
I liked the Thief soundtracks. That music always sounded good for Garrett's work, and each mission had its own track. Shalebridge Cradle was especially good, and Shipping--And Receiving will always stay with me.
Perfect Dark had (and still has) one of the best soundtracks of any game ever made. Of course, it was also one of the most incredible and, by many standards, best games ever made, especially considering how advanced it was for the time it was made in.
I mean, all that glorious music on an N64 game? If that doesn't strike you as impressive, then you didn't let it hit you hard enough.
I think the video game Heavy Rain had great music. It is somewhat sad, but it matches the game perfectly (I find it funny that that is pretty much what every body else said: [fits] the game perfectly).
Let me be the first to say, (shame on you guys!) The Elder Scrolls III: Morrowind. I practically nostalgia all over myself every time I hear the main theme and the rest of the music aint bad either.