A group has created a levitating quadcopter consisting of 4 motors and 4 spinning magnetic arrays. By spinning the magnets over a copper sheet, the 105-lb quadcopter levitates. The magnetic levitation is so strong that pressure on the top won't push it down.
The spinning magnets induce currents in the copper sheet, which creates a magnetic field. The magnetic field is a mirror image of the field in the magnets, so they are repelled. When the rotors are able to spin the magnets fast enough, the repulsion leads to levitation. While this looks like a simple make-it-yourself experiment, it is quite difficult to build.