This is a jumping robot created with nothing but a dc motor, wooden dowels, popsicle sticks, rubber bands, and string. Watch on YouTube.
The dc motor pulls in the string which gives the rubber bands stored energy. At the bottom, string is glued to a small piece of cardboard which gets ripped off once the tension in the string is too much. This releases the rubber bands and launches the battery up, pulling the entire contraption with it. This robot was able to jump 7 inches with the current rubber band set up!
Without redesigning the robot, a quick way to get more height would be to add more rubber bands for more stored potential energy. The release mechanism would have to be a little stronger than it currently is since it gets released before the contraption reaches the bottom.