I enjoy many different video game music although I do enjoy music from the Sonic games, I even have three of the games’ soundtracks:
Sonic Adventure 2 soundtrack
Sonic Heroes soundtrack
and my favorite Shadow the Hedgehog vocal trax! 
(yeah, I know, I’m a Shadow fangirl <3 )
What? No Banjo-Kazooie in this thread? Such blasphemy! 
Well I love that game’s music. Same for Diddy Kong Racing, Conker’s Bad Fur Day, Donkey Kong Country series, and… practically anything else by Rare.
I have all three DKC games, that series does have some pretty awsome music as well. 
Pretty much any mario game.
Smash Bros Brawl
Smash bros melee
Super Mario Sunshine
Super Mario Galaxy etc…
Awsome, a mario game, one of my favorite music from that game is the Super Mario Bros. theme, a classic.
I like all of the old (like, ancient) video game music, like Kid Icarus- The Underworld, Duck Hunt, Donkey Kong, Excite Bike, and Pac-Man, and I’ve never even played any of those games! Except Pac-Man, but I always die at level 1. 
I’m also a fan of the Mii Channel music, Mute City from F-Zero, and of course, any Mario music.
ohhhhhh my goodness. Where to start… I mean, Where!? There’s way too many video game songs I like that I don’t think I can list them all… So I’ll just settle with soundtracks. 
One of my absolute favorites are both the US and Japan versions of the Sonic CD Soundtrack.
Also under the Sonic name are Sonic 3D Blast (The Sega Saturn Version…), Sonic R, Sonic Rush and Sonic Unleashed. And more… (lol)
Man, I love all the Main Mario soundtracks. My favorite Main Mario soundtrack at this point has to be Super Mario Galaxy.
More Mario soundtracks I love… Super Paper Mario, Mario and Luigi Superstar Saga, Mario 64, Super Mario Kart… And of course, more.
Now, on some not-so-big names. Here’s just a few soundtracks I love that aren’t exactly as well known.
The whole Donkey Kong Country series has good music…
Banjo-Kazooie and Banjo-Tooie are great…
Kirby Super Star is not only what got me into Video Gaming, it’s also got a great soundtrack.
The Nights Intro Dreams soundtrack is great. 
Man… there’s so many good soundtracks… Hope that gives anyone curious a good look into good soundtracks.
Has anyone else here played Okami?
It’s not only stunningly beautiful, but also features some of the best music I’ve ever heard, video game or otherwise.
Examples:
I know I’m coming in late to this (don’t I usually?), but this is a topic near and dear to my heart.
I like a number of soundtracks folks have posted, especially the Final Fantasy ones, but I wanted to give props to a few PC-based games that most people may be unfamiliar with.
Fantasy General. This game came out in 1996 where redbook audio games were coming into fashion, and it may be one of the best examples of the those. Redbook audio CDs are regular 70-minute audio cds, but the first track is a data track instead of a music track. So the first 100MB of the disk would be game data, while the other tracks are music tracks. The game installs on the hard drive and then plays the CD as a music CD (which it is). This was stunning at the time since before then all you could get was crappy soundblaster music synthesis, while Redbook games could feature full orchestras on an audio CD.
Fantasy General was one of those games that used the orchestra and full choir to an astonishing degree, taking a few original compositions along with a number of classic 11th century mass songs as well as a Bach piece. Highlights:
Fantasy General - Battle KeldoniaThis theme plays during your first battle sequence at the start of the game, and it’s the perfect accompaniment for a cavalry charge!
Track 4 - Let All Mortal Flesh Keep SilenceThis is probably my favorite track. Simply amazing.
Victime. This, along with Battle Keldonia above is from singer Marisa Lenhardt’s own website!
And finally… Victory! One of the best Halleluja choruses I’ve heard.
Heroes of Might and Magic II. Not as obscure as Fantasy General, Heroic of Might and Magic was a deservedly popular strategy RPG for the PC. It was another Redbook audio title, this one featuring operatic music. This is hardly your usual game music.
Wizard Castle
And also: Barbarian Castle
And from Heroes of Might and Magic III:
Stronghold!
Many more. I actually couldn’t find the themes I really liked, but this gives you an idea.[/url]
A few more music pieces to add…I’m really liking some of the level music from Sonic Unleashed and I would have to say that some of the music from Legend of Zelda Twilight Princess as well…
The Entire Cave Story Soundtrack
The Mother 3 soundtrack, especially this.
The Mother soundtrack.
The Earthbound soundtrack.
There’s a lot more soundtracks I like, but I can’t think of them at the moment. I will update this post.
I have to agree, especially Midna’s theme and the music from the rafting mini-game are brilliant.
Kingdom Hearts 2- Sanctuary
[url]http://www.youtube.com/watch?v=nbnD7sVCBOE[/url]
Sonic CD- Sonic Boom
[url]http://www.youtube.com/watch?v=LJXKoubh9sQ&feature=related[/url]