In 1994 Andrew Alcon patented* a simple device which stably levitates a magnet above two counter-rotating aluminum rotors.
The motors used in this demo are 5,000 RPM, 1/15 HP, 115 VAC Dayton model 2M066. The aluminum rotors are carefully made to spin true. A light dimmer circuit is used to control the speed of the motors.
*US Patent 5,319,336
The small floating magnet is balanced against gravity by the upper ring magnet. This levitation configuration is unstable vertically, but stability is provided by the diamagnetic carbon plates above and below the floating magnet. The diamagnetic material produces repelling forces as the floater approaches, pushing it back to its center position and overcoming the vertical instability.
A small sample of a type I superconductor will demonstrate the Meissner Effect (levitating a magnet) when cooled in liquid nitrogen.
Another example of superconductivity can be demonstrated using a type II superconductor.
A piece of superconducting material is cooled with liquid nitrogen on top of a track array of magnets. When the superconductor cools, it floats atop the magnetic array. If the track is turned upside down, the superconductor goes from being levitated to suspended due to flux pinning which freezes the magnetic flux within the type II superconductor.
Video of diamagnetic levitators showing many objects including hazelnuts, strawberries, and a living frog.
An electromagnet suspends an iron ball in mid air. An IR LED and phototransistor pickup senses the position of the ball, and the associated electronic circuitry controls the current to the magnet by active feedback. Two other magnets 90° apart and 90° out of phase can cause the suspended ball to spin.
Links:
[1] http://www.physics.ucla.edu/marty/levitron/