Paper plates, Popsicle sticks, and a balloon are all you need to play Balloon Ping-Pong. (Not sure how sturdy the paper plates would be, but may be able to do something similar for a carnival/game night social event theme.
Beach Ball Race- kids work together to hold beach ball between their backs for the first leg of the race, then their sides, then elbows. The field Day Challenge is halfway down on web site includes water relay, tricycle race, and tug-of-war. Check it out!
Pantyhose Bowling This was a quick and easy game where you place a softball in a pair of pantyhose and team members wrap it around their forehead. Players have to make their way down the line knocking over water bottles with the softball.