Some months ago I was searching for music from video games, and I found VGMusic, which wound up being a pretty handy resource. Especially with some of the more popular games, there are multiple versions of a particular piece uploaded onto the site, so it's interesting to compare the variations. Which ones are the same as it was in the game, does it sound better using a guitar, or a piano.
What I find frequently, though, is the feeling something's missing. In some cases (Halo's opening theme) what's missing is voices, since it's strictly instrumentals on the site, no singing. More often, I realize that it's not matching up with my memory of the song, because I remember it from when I played the game, and it wasn't just the music I'd hear then.
When I listen to "New Junk City" from Earthworm Jim, I keep expecting to hear the sound of Jim bouncing on piles of tires accompanying the music. If it's a level of Goldeneye, I remember it with the occasional silenced gunshot mixed in (the levels Bond had a silenced gun, anyway). With a racing game I keep thinking I'll hear engine noises and so on. But those are sound effects, not music, so they wouldn't be included. Even if they were, in the case of shooting, when the sound would appear in the piece would vary with the individual player.
I find it kind of neat that in my recollections, the sound effects are part of the music for me. It makes the music almost alien to hear it without the noises of the actual gameplay.