A theorem due to Earnshaw proves that it is not possible to achieve static levitation using any combination of fixed magnets and electric charges.
Static levitation means stable suspension of an object against gravity.
There are, however, a few ways to levitate by getting round the assumptions of the theorem. In case you are wondering, none of these can be used to generate anti-gravity or to fly a craft without wings or jets. The proof of Earnshaw's theorem is very simple if you understand some basic vector calculus. At a point of equilibrium the force is zero. If the equilibrium is stable the force must point in towards the point of equilibrium on some small sphere around the point.