Quasi-free-standing epitaxial graphene is obtained on SiC(0001) by hydrogen intercalation. The hydrogen moves between the (6 square root(3) x 6 square root(3))R30 degrees reconstructed initial carbon layer and the SiC substrate. The topmost Si atoms which for epitaxial graphene are covalently bound to this buffer layer, are now saturated by hydrogen bonds. The buffer layer is turned into a quasi-free-standing graphene monolayer with its typical linear pi bands. Similarly, epitaxial monolayer graphene turns into a decoupled bilayer. The intercalation is stable in air and can be reversed by annealing to around 900 degrees C.