Ticket to Ride is a great board game for the family. Each player is given several secret destination cards, and you all must build a continuous train between each city listed on the cards. Some routes have allow multiple trains to go through at the same time, sometimes you have to go around blocked routes, and you have to complete your trains before your opponents do.
We played this with the kids, and they had a great time. You can play this game in about two hours or so.