I had a chance to play several games last week that were fun, fast, and family friendly. One, Garden Dice, is pretty ideal for all ages. The second, Fleet, is better for older teens who can calculate and manage "economies."
In a game of Fleet you create and manage a fleet of fishing vessels in Nunavut, Canada. Players can buy boats and fish for shrimp, lobster, tuna, or other sea thingys. Players can also invest in wharfside pubs, casinos, and fish processing ships. The winner is the person who can land the most fish and generate the most victory points.
Fleet's main game mechanism is a set of auctions. Players bid for "licenses" to seek out certain kinds of fish. A license will also allow you to get some in-game bonus. One key to the game is to bid for the best licenses and not pay too much. The other key is to most efficiently create your fishing fleet and then catch lots of fish.