Credit to the OP because this is a great idea for a thread... So for me it's Grand Theft Auto 4 because I'm a GTA 4 fanboy. If I had to pick out two songs that define that game for me, it goes like this.
This one is the trailer theme, it's a perfect song and it plays at the end of the game too.
This is one of my favorite songs in general. I found it while scrolling through the random in-game radio stations one day and had never heard it before, I was blown away at how good it was. It sounds relaxing but it's also kind of tragic and it fits the game really well. In GTA San Andreas they have a different version of this song that's covered by Ice Cube and it's also really good.
Obviously I have to shout-out other franchises, The Legend of Zelda Series, Various Final Fantasy games, Assassin's Creed, Fallout, Half-life, anything by Jeremy Soule, all amazing music. Assassin's Creed 2 in particular has one of the most beautiful soundtracks I've ever heard.