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On the pinball side of things, 1989's Black Knight 2000 and 1993's The Twilight Zone were known for having one of the best soundtracks ever for a pinball game. The latter game uses Golden Earring's 1982 hit song "Twilight Zone" as its main theme.
Super Hang-On had four great songs: Outride a Crisis, Sprinter, Winning Run and Victory Road.
Gyruss (in its initial arcade form) only has one recurring song, a remix of Bach's Toccata and Fugue in D Minor, but hearing the song in stereo sound on an '80s (!) -era arcade machine will make you say "Whoa!"
For a game about murdering other assassins to jammin'jazz tunes, the ending theme to The Outfoxies, "Enjoy Life" is as chilled and lovely a piece of jazzy piano as you'll ever find.