Overview - All the songs I'm listing are from Bioshock because it is the embodiment of an iconic game and its music follows suit.
Bioshock - Welcome to Rapture
Why - Anyone who's played the Bioshock demo (and if you haven't, please do it quickly) can see why this piece (the intro as you descend in the bathysphere) is so amazing. It's the song that really embodies the game, as it's the first thing you here when you see Rapture.
Bioshock - Cohen's Masterpiece
Why - You hear this, and immediately you realize that it's Sander Cohen only put to sheet music. It starts softer, like Cohen first speaking to you, then grows louder and more frenzied as does his voice. It's a piece you HAVE to listen to if you enjoy solo piano music.
Bioshock - Dancers on a String
Why - This song feels like it represents the story of everyone in Rapture. It's sad, the melody played on a violin with the piano soft in the background, and you can almost see a once beautiful city that's crumbled into the remains before you and the citizens reduced from the once Cream of the Crop of the world to insane people spliced and muttering gibberish.
All of these songs were just released today for free by 2K. I'm listening to them as I write this. They're all amazing and any fan of games should listen to them.
http://www.2kgames.com/cultofrapture/home.html