It might not be as elegant or technologically-advanced as a Segway or a motorized unicycle, but this easily constructed 2-wheeled robot might be a fun project for a free afternoon. The heart of the balancing mechanism is an SPDT switch with a button cell attached that reverses the motor when the robot begins to tip in one direction. It's not controllable and it tends to fall over quite a bit, but it's a good starting point and could be refined by lowering the center of gravity or figuring out a simple way to change the motor speed based on how far the robot has tipped over. There are no accelerometers or tilt switches so the components could be sourced from a parts bin, and its simple design definitely leaves a lot of room for improvement.
