Red Dead Redemption featured an original soundtrack. It was mainly instrumentals, but there were four songs with lyrics that played at certain key segments. Upon entering Mexico, you were treated to "Far Away" by Jose Gonzalez, which was a very cool moment in the game.
"Compass" by Jamie Lidell was another stirring song that played at a certain key (and emotional) segment.
"Bury Me Not, on the Lone Prairie" by William Elliot Whitmore also featured at another major scene.
"Dead Man's Gun" by Ashtar Command, played at the credits. Not quite as powerful as "Compass" but context is everything.
There are a number of songs by this group made specifically for STALKER. The singing isn't the best, but the game is very immersive and this song features prominently in it. Listening to it takes me back to my first playthroughs of the game.
This game had several songs written for it, and they were an integral part of the game. They were not great songs, and at least one was painfully bad (the one with male vocals). But regardless, it's still one of the best video games I've ever experienced and I wish the sequel had not been canceled.
If you retrieve the band's lost instruments via typical hack-and-slash game questing (ie, kill some stuff), they give you some (not great) weapons and invite you to a concert, which leads you to the following video (you can come back and replay it, too). Cute song. Didn't like their other music as much, though, sadly.