Sure, there are a few Ennio Morricone sound-alikes kicking around in there, but who cares? It's the Wild West, baby.
Wild Arms - Into The Wilderness
The Legend of Zelda: Ocarina of Time - Gerudo Valley
Rising Zan - Johnny No More
Bastion - Spike in a Rail
Red Dead Redemption - Far Away
God Hand- Bronco Buster
Freddy Pharkas Frontier Pharmacist - The Ballad
Outlaws - Anna's Theme
Oddworld: Stranger's Wrath - Fighting Outlaws 1
Gun - Theme
And credit to twitter user @OmegaLiquidX for suggesting the idea!