Supposedly there's a proof that you can't make a permanent magnet bearing that's stable in all six degrees of freedom (up/down, right/left, front/back, roll, pitch, yaw) for a non-moving object. (You can levitate objects while they're spinning but they have to touch down or you need an active system.)
Has to do with the divergence of the mag field being zero, i.e. no monopoles. (Wonder if that means you COULD make a stable levitator if you had monopoles, and/or that you could levitate a charged object?)