Hmm. I THOUGHT I had answered this somewhere else - if I have, excuse my redundancy.
The first arcade game I ever played was Gunfight, played at a class trip to Space Farms. The class trip sucked, but the game room, adorned with pool tables, ping pong, and GUNFIGHT, was quite memorable, even to this day.
The first home game I ever played was - yes, the Odyssey. I'm not sure which one I played first though I think we had the home game first. I'll never forget taping those plastic color overlays to our TV screen. My parents weren't real thrilled with that. It wasn't long before I had my OWN TV because they had heard that this game and other "pong" games would ruin the TV screen. w00t!