When I was little my Mom had an Atari that she and I would play all the time. Even my Grandma played, but she'd only play Pac-Man.
Then, when I got a Sega Genesis, my Mom played that as well. She mostly played The Lion King or Samurai Showdown with me.
Then, Nintendo 64 came around and it was Super Mario 64, Glover, and Diddy Kong Racing.
PS1 was this one disc that had classics like Pole Position and Pong on it, so we played that, Tetris, Break Out and some Two Player fighting games.
More recently, it's Mortal Kombat, Dead or Alive, and even Knights of the Old Republic (I'm surprised with that one)