The most common blindfold game is Pin the Tail on the Donkey, but there are numerous others, including Duckie Wuckie, Blindman's Bluff, Is That You Moriarty?, and obstacle courses. Many games that include having players close their eyes could also be considered blindfold games.
Pin the Tail on the Donkey is played by having a target, typically an illustrated donkey, facing away from the players and the person who is blindfolded while holding a tail with a pin in it. The player tries to pin the tail as close as possible to where it should actually go. Duckie Wuckie, also called Squeal Piggy Squeal, is a game where the person who is blindfolded is in the center of the circle, and that person must identify the other players simply by a few words that the other player says in any voice he wants. Blindman's Bluff is similar, but the blindfolded player must identify the other players using only his sense of touch.
Is That You Moriarty? is a blindfolded duel with household items used as swords. The first blindfolded player to hit his opponent wins the game. The last option, obstacle courses, will take more time to set up, but they can be incredibly fun. The blindfolded player has to navigate through a series of obstacles while trying to finish the race before the other competitors. To turn this into a team game, they can each have a coach who is not blindfolded telling them what to do or where to go.