Thanks to all the readers for their good ideas. Here are some of theirs and some of my own as well:
1. Paper-Airplane contest. Distance and/or accuracy.
2. Building a bridge with straws/Popsicle sticks, etc. The one that can hold a certain amount of weight for the longest time wins.
3. Scavenger Hunt
4. Water Balloon Toss. You know the one where 2 people face each other and toss balloons back and forth and see who can get the furthest apart?
5. Foursquare competition
6. Egg Drop
7. Building the highest tower possible out of straws in a certain amount of time.