I'll start off with Raiden II's Repeated Tragedy.
A local restaurant had this game, and every time we went, I'd beg my parents for money so that I could play it. I wasn't very good at the game, so I never got past the first stage, and so I heard this song a lot. Really gives me nostalgia.
Also got to shout out Streets, from Timesplitters too. I put a lot of time into this game as a kid, and this song is what got me into futurepop (love me some VNV Nation).
I probably spent so much time during my formative years (and some of my adulthood) playing Age of Empires II and Age of Mythology that these were the only ones I could remember off the top of my head. Many others I can remember if I think about the game, but not as easy.
Also, Asylum Demon, Firelink Shrine, Ornstein and Smough and Gwyn Lord of Cinder from Dark Souls 1. I've probably beat that game dozens, if not hundreds of times, and have used a ton of playthroughs as background noise before going to bed.