I am teaching a US citizenship class for US immigrants at a fairly high level of English ability. I have a simple but great game called "Who Am I"? Here's how it goes.
I photocopied faces of American Presidents and famouse American heros such as Martin Luther King from encyclopedias. Without showing the students the photos I ask them to come to the front of the class, turn their backs to me, and face the empty classroom ( I only have about 6 students). I then tape the photos to their backs. The goal is to have to the students guess who they are. The students accomplish this by "mingling" around the room looking at each other's backs asking questions of each other which are meant to give clues regarding their identities. They are not allowed to tell each other who they are. For example, if you have a photo of George Washington on your back a student may inquire, "say, weren't you that chap who cut down the cherry tree"?

When you know who you are you can sit down. Those sitting must coach the ones standing. When everyone is seated, they remove the photos and read the backsides of the photos silently to themselves. The teacher has written a few key facts about the person in the photos. Then, one by one they give a brief presentation to the class about who they are and what has made them famous! Fun.