Blokus might be the easiest game to teach others. Players take turns placing their Tetris-like pieces on the gameboard. The only rule is that your pieces have to touch, but they can only touch at the corners. The first player to place the most, or all, of his or her pieces on the board wins the game.
The beauty of this game is that you can play right out of the box. Even the youngest family members will grasp the rules, and yet the game offers a challenge to every player. Every game is different from the last, so your family will not outgrow this game anytime soon!