If playing in an actual arcade, or placing the game as a moment in time, it would be something from the Street Fighter 2 family (preferably after Turbo sped up the game). Gameplay was awesome, but it was the social interaction and camaraderie that developed among players inside the arcades that sets this game apart for me. People lining up to play, usually against other people instead of against the machine, and always talking - trading tips and moves, blustering and boasting. I had never experienced anything else like it from an arcade...
But if getting something for my home to play with friends, it would probably be something easier to get into. TMNT almost gets the nod, but is edged out by the massive double screen and support for more players in:

Note that this assumes you are talking arcade
video games. Otherwise I would go pinball without any question. There are at least a dozen titles that I would love to own and choosing between them is impossible. Maybe Taxi?