My dad use to enjoy chess. Weldon and I both wanted to learn chess as fast as we could, so we could challenge him.
We also had a game we called marbles. This is not the traditional marbles game. My dad had taken a piece of plywood, and then with a drill press had made impressions around the board, something akin to Parchessi or Trouble. We spent a great deal of time with this game, and used two die to control movement. Of course doubles you got to go again, and if you landed on someone they had to go back to start.
Another family favorite was Monopoly. My dad was very good at being a tycoon. I don't remember ever winning a family game of monopoly.
As we became a bit older, Rook became our family game, and a version we called Mormon Bridge, which was similar but different. I guess all families have their own rules, in ours the rook was the high trump and worth 20 points. Ones were higher than a 14 and worth 10 points. You had to trump if you could. We would often have lengthy rook battles; especially during holiday season. Mormon Bridge was fun because you had to guess how many tricks you could win, and were awarded, or lost points based on your guess and how accurate you were.