Our family loves to play games. It's a little challenging with our 18m old, so sometimes she sits in our laps and sometimes we play after her 7pm bedtime.
One of our favorites is Uno. We've been playing since our youngest son turned two. It's a great way to teach color and number recognition, matching, strategy, and taking turns. Everyone lays their cards out in front, and we help each other figure out the best moves. We skip the challenge of remembering to say "uno" with only one card remaining, because it's a little too difficult for the younger kiddos to grasp. When someone wins, we all give high fives & say 'nice job'. Then we shuffle and deal the cards to start again, saying "You never know who will win next time!"
We usually play 2-4 games in a setting, but my kids would be happy to play 10 games in a row!