Music in games tends to come in a few flavors: Epic Orchestral, Modern Metal, and Pulsing Electronica. It's effective at keeping you pumped up ready to kill, but it doesn't have much emotional range. Some developers are starting to broaden their horizons, putting audio at the forefront and creating soundtracks that don't sound like "game music." My favorite gaming moments of the past few years have been thanks to lyricized songs in games-- particularly when its a song that sets a very specific mood. Red Dead Redemption did this in a few very powerful moments, and Bioshock Infinite does it pretty much non-stop.
So lets have some fun! What non-videogamey songs do you want to hear an a game? Extra credit if you can briefly describe the real or imagined game, and where the song would fit in.