There's a theorem that you can't get stable levitation with any
classical collection of magnets, charges, gravity, etc. You can get
stability only if you allow forces that classical mechanics can't
explain. These include contact forces between objects, but I don't
think that's what you're interested in. It's no surprise that you can
support something by putting it on a table.
Another type of force that doesn't make classical sense is
diamagnetism- the tendency of some objects to be repelled by magnetic
fields. Most of us are weakly diamagnetic. Diamagnetism allows stable
levitation. I've seen photos of very tiny frogs levitated stably by
strong magnetic fields, but that's impractical for larger objects.
However, many superconductors are very strong diamagnets, avoiding
magnetic fields altogether. Superconductors can indeed be stably
levitated, as can magnets near superconductors.
No one has ever found anything with a net magnetic charge, where
the Northness and Southness don't exactly cancel. We have a name for
these hypothetical objects, if they ever show up: magnetic monopoles.
Some theories of the early universe say that there should be a very
small number of these monopoles around.
(published on 10/22/2007)