My personal favorite family game for the Wii is Super Smash Bros Brawl. This is an incredible fun, addicting and competitive game for all ages. A few other honorable mentions go to Mario Kart Wii, Super Mario Galaxy 2, Donkey Kong Country Returns, Rock Band 3, Wii Sports Resort and Punch-Out.
I know it sounds strange, especially for teenagers but Mario Party. It's not the characters or the gameplay, it's the competition. It's a great game for the family, and boy it can get exciting when you want to win!
Anything with Mario on the box, honestly. You can get hours upon hours of fun out of virtually any Mario game, whether it's Kart or Smash Bros. or Party or just one of the normal Mario platforming titles. I'm a little sick of the plumber after so many years, but Nintendo always seems to put on its A game when they release a Mario title.
The game isn't new, but I had so much fun playing Smash Party with my family. It was a great way to involve the kids as well. I think this was the only game that my entire family enjoyed playing together, other than wii sports and things like that. You really can't go wrong with a Super Mario game.