I realize I was a bit slow with this one. There is a small chance you've already heard of Dear Esther. But I've just now stumbled upon it myself. Regardless, for such an amazing and unique experience, one more recommendation can never hurt.
The game is littered with beautiful music.
Dear Esther is a Half-Life 2 mod. It's a free game, and I believe only took me about 2 hours or so to beat. The similarities to Half-Life 2 are limited to the engine and the first person view perspective though. From there on out, Dear Esther is if anything, more comparable to Braid, for they share unique storytelling methods and slightly disturbing themes.
Dear Esther is a story driven first-person adventure game. At least that's how I would describe it. It's possibly one of the slowest paced games I've played in the recent years, yet it's no doubt one of the most interesting. It's full of beautifully disturbing music, haunting scenery, and chilling atmosphere, all brought together with a story that is worth listening to. I would give you a loose outline of the plot, but I believe that listening, exploring, and interpreting the story based on what you find is what the game is all about.
So if you're in the mood for something different. Slow, sad, meaningful, and very atmospheric then go give "Dear Esther" a download (It's free, c'mon!). You do need Steam, and since it is a mod of Half-Life 2, I believe you need some form of that as well. I was able to play it with only HL2 Deathmatch installed.
Dear Esther, should not be viewed as a traditional game. It should be viewed as an example of what games can do. The feelings they can bring, the stories they can tell, and the experience only they can give you.
Download "Dear Esther"