My mom would play Super Mario 64, and the Crash Bandicoot games on the Playstation with us when my brother and I were kids. She and my dad would play arcade games with us like Dig Dug, Galaga, and this weird Centipede game on the PS. There was also Mario Kart 64 and Double Dash, Super Smash Bros and Melee and Pokémon Coleseum.
They also played the crash mode in Burnout 3, Wii Sports, Links Crossbow Training, Mario Kart Wii, and some other Wii games I can't remember with us.
Now they might play Mario Kart 8, but they pretty much say that since my brother and I always win they just focus on racing each other. They won't come near Smash 4.
I did beat Halo 3 with my mom though, and now she plays Animal Crossing New Leaf with us.
Besides all that my dad only ever played fighting games with us.