This is really simple and surprisingly fun. We played it at the Life is Good Conference and everybody enjoyed it. Sometimes the simplest games are really the best.
This is a two-player game.
Player A says a number between 1 and 10. Player B has to say the number that comes after it, very quickly. (A rhythm of 1/2 to 1/3 second for each response is good, you can clap together to get the feeling of a rhythm.)
Then, Player A has to say another number, keeping the same rhythm. (It can be the same number or a different one, but not the next one.). Player B has to say the number that comes after THAT number.
Back and forth it goes, until someone makes a mistake. At that point, start over with roles reversed.
Mistakes: Player A makes a mistake if he takes too long to think up a new number, or if he mispronounces a number, or just counts up one more. Player B makes a mistake if she takes too long to think of the number she should say, or if she says the wrong number.
Scoring: A mistake counts as a point for the other player. First person to a certain number of points wins. (Scoring is optional, you can just keep playing back and forth indefinitely).
Advanced Play: If you get really good, set a certain number of correct responses which will result in a point for Player B. (15 or 20 correct responses are easy enough to count on your fingers.)