Our family has always enjoyed playing different card games together. When the kids were small we would play games like "Go Fish" or "Crazy Eights". Even young children can learn these games. And they love to feel big playing big kid games.
There are so many card games that can be learned as the kids get older as well. I have even taught my kids different variations on Solitaire. That way, when family night is over, they can still have fun playing cards, even if no one else is available to play.