Purpose Games is a free service that allows users to create custom games, share games, and play games. You can create and play two styles of games on Purpose Games. The simpler of the two styles is a multiple choice game. The other style uses images and maps on which players have to name the places represented by placemarks on the image or map. For an example, try this game about clouds.
Purpose Games gives game creators the option to make their games public or private. If you select the private option, only the people to whom you send invitations will be able to play your game. You can even have students create their own review games!