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 haven't played Dota 2 in maybe 10 years, and when I read your post I could hear it in my mind.