Ehhhh.... I think it was Shinobi at a local pharmacy. Or the Michael Jackson Moonwalker machine that was parked right next to it. Good times!
Edit: The first game I played in my own home was a game called Movie Monster by Epyx for some kind of old Apple computer we had when computers were first making it into the home scene. Movie Monster was amazing. You picked your favorite monster whether it be Marshmallow man, Godzilla, The Blob, Mothra, or a slew of others and just went around destroying the city a la rampage style. Soooo fun!