Life is Beautiful from Deadly Premonition. FK in the coffee, indeed.
Escape From the City from Sonic Adventure 2.
I'm not even a Sonic fan, that song just burned itself deep into my grey matter.
The Super Mario Bros. theme.
I mean that song is the essence of childhood gaming to me, even though I only played SMB1 way later in life.
This is True Love Makin' from Capcom vs. SNK 2.
It might drive you crazy after a while with the way it loops, but holy hell, I kind of love this song.
The character select theme from MvC 2, aka I Wanna Take You for a Ride.
Again, it might drive you crazy, but once it's in your head, it's there to stay.
There's also the memetic virus that is the Buck Bumble theme song, practically the entirety of the SF3: Third Strike soundtrack (Elena's and Ibuki's themes in particular) and and and, but I don't want to spam too many links.