Space Invaders!
This game almost needs no introduction. It is the classic arcade game by Atari, Space Invaders. You are a green tank moving between shields trying to shoot the little bug-like aliens. The aliens pick up speed as the move down the screen. If you hit the red spaceship you get more points.
I really like this game because, unlike most games around this time, it kind of has a nice rhythmic/musical element to it. It reminds me of the music in Mario that speeds up when time is close to the end. I got a chance at the 2013 Indiana State Fair to play this game on the arcade version. I played two-player with my mom. Needless to say she won, it is one of her favorite games.