I grew up playing the original NES with my grandparents but we always break out the board games when we have larger family gatherings, everything from Trivial Pursuit to UNO. My wife and I play computer games together, and my brother and I like to play console games together.
We play loads of European board games like Carcassone, Agricola, The Village, Dixit, and (my favourite) Seven Wonders. We also play a lot of FFG and Games Workshop games: Chaos of the Old World, Warhammer Invasion, Warhammer FB and 40k.
We boardgame a lot and one of our favourites together is the pathfinder card game. Because we each have a character that stays with us game to game that we build on it means if you miss a game you're a tad behind so in a way forces us to play. But we absolutely love it!