Special shout-outs to a few of my all-time favorite tracks, beyond just video games:
TESV: Skyrim: Kyne's Peace
Hands down my favorite Elder Scrolls track, a series brimming with great music. A phenomenal, emotional piece that really drives home the tone it wants to convey. This tune is perfect.
Half-Life: Vague Voices
My favorite Half-Life track, a series which has its own fair share of great music. It's the one that plays at the very beginning of the game, and is easily one of the most atmospheric and tone-setting pieces I have ever heard. I didn't get to play Half-Life when I was a kid--I only first played it in 2013--but hearing this track for the first time was incredible.
Quake 2: Descent into Cerberon
If this doesn't get you pumped for action, I don't know what to say. I really wish the soundtrack worked automatically for my version of Quake 2, as tracks like this would have amplified the already great gameplay, but still I have played this track too many times to count.
Unreal Tournament: Foregone Destruction
Unreal Tournament was also another boat I unfortunately missed out on when I was a kid. Thus, I've never really gotten to experience UT's true potential. But it has some fantastic tracks, although the original single-player Unreal is my all-time favorite video game soundtrack.