The levitron is a device for levitating a magnetic top in the air above a strongly repulsive magnetic base. Ernshaw's theorem states that no static arrangement of free magnets (or charges) is stable. But this system is not static. The top spins and must conserve angular momentum. Thus it is stable to flipping over for a certain range of angular velocities. This takes practice and would work better if I had the starter (or the Perpetuator add-on).
Berry, M V, 1996 Proc.Roy.Soc.Lond A452, 1207 - 1220, The LevitronTM: an adiabatic trap for spins.