A magnet or properly assembled array of magnets can be stably levitated against gravity when gyroscopically stabilized by spinning it in a toroidal field created by a base ring of magnet(s).
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Scientists have discovered a way of levitating ultra small objects by manipulating the Casimir force, which normally causes objects to stick together due to forces predicted by quantum field theory. This is, however, only possible for micro-objects.
While we don't have our hoverboards just yet, we do have the very real phenomenon of quantum levitation, which is almost as good. Under the right circumstances, a specially-made material can be cooled down to low temperatures and placed over a properly-configured magnet, and it will levitate there indefinitely.