These are all games that require at least one of the players to be blindfolded.
Pinning the Tail on the Donkey
This has been a party favorite for longer than you might think, and it has many variations. The traditional version requires a picture of a donkey without a tail, tails drawn and cut out of a separate piece of paper, something that will help the tails to stick to the picture (traditionally, it was a pin, but glue or rubber cement could be less sharp and pointy alternatives), and a blindfold. There are commercially-made Pin the Tail on the Donkey sets available at party stores, or you can make your own.
The picture of the donkey is hung on the wall at a convenient height for the players. You can use just one tail many times over, or you can have separate tails for individual players. If using several tails, mark the tails with numbers so that they can be told apart later. (I prefer having several tails and leaving them all stuck to the picture until the end so that they can be compared.)
One at a time, players stand about six feet away from the picture, blindfolded and holding one of the tails (Beaver 42). Now, the blindfolded player has to find his way to the picture on the wall and stick the tail where he thinks it ought to go. Hardly anybody will get it in the right spot, but the person who comes the closest is the winner (Beaver 42).
Ruth and Jacob
This game is similar to Marco Polo, but it isn't played in a swimming pool. One person is chosen to be "Jacob" ("Jacob" can be a girl, it's just a title so it doesn't really matter) and is blindfolded. The other players stand around "Jacob" in a circle. "Jacob" points at someone (a random person since "Jacob" can't see), and that person becomes "Ruth" ("Ruth" can be a boy, like "Jacob", it's just a title). "Ruth" enters the circle, and "Jacob" calls out the name "Ruth" and tries to find "her." "Ruth" tries to keep away from "Jacob" without leaving the circle, but every time "Jacob" calls out the name "Ruth," "Ruth" has to call out the name "Jacob," giving away her location. Once "Jacob" manages to catch "Ruth," he has to guess who he's caught without taking off his blindfold. If his guess is right, "Ruth" becomes the new "Jacob," and the game continues. If his guess is wrong, he keeps the part of "Jacob," and everyone starts the game over until he gets it right (Greenaway 61).
This game doesn't actually involve a blindfold, but I included it in this section because it is kind of a less active version of Blind Man's Buff, and it does involve a player hiding his eyes. It reminds me of a game I used to play in school called Heads Up, Seven Up (not exactly the same, but similar).
One player kneels down (or sits, whichever is most comfortable) and hides his eyes, resting his head on a chair, couch, or table (whatever is convenient). This person puts one of his hands behind his back, palm up, while the other players stand behind him and take turns slapping his hand. The player whose hand is slapped has to try to guess who did it. If he guesses correctly, that person will take his place (Beaver 42).