Split the group up into two teams. You can either go to a local maze or build one yourself. If you are building one yourself, have one team build the maze with rope or chairs. Take the other team and blindfold them. There are two ways you can do this exercise. One, is the blindfolded team can use their hands to follow the rope around until they get to the end. Or, pair up the blindfolded and non-blindfolded people. Have the non-blindfolded person guide their blindfolded person through the maze with verbal commands. After they get through have them switch and do the exercise again. This helps build trust within the group.
This exercise shows the team how to work together on a common task. This task involves taking a PVC pipe and a ball that fits in the pipe, cutting the pipe in such a way that it will only fit together in one way. Have a start point and an end to where the pipe must flow. Once the team reassembles the pipe they will drop the ball down to see if it goes from one end to the other without dropping. Add twists and turns and obstacles that the team has to overcome in order for the pipe to fit together.
Take a story and tell it with pictures. To do this, give each team member a picture. Each member cannot reveal his or her picture to anyone else. The group has to figure out the sequence of the pictures in order to tell a story. Each person will have a different spin on his or her picture and the group will have to figure out how these pictures fit together.
Sporting activities can get the group to work together and reveal who among them is a group leader. The group will have to deal with the dynamics of multiple people trying to lead the rest of the group and people that aren't willing to participate. Try playing volleyball, basketball, football or soccer. Observe who rises to a leadership level and then take those people out the game for a quarter or an inning to see how the group compensates.