Density functional calculations of electronic structure, total energy, structural distortions, and magnetism for hydrogenated single-layer, bilayer, and multi-layer graphene are performed. It is found that hydrogen-induced magnetism can survives only at very low concentrations of hydrogen (single-atom regime) whereas hydrogen pairs with optimized structure are usually nonmagnetic. Chemisorption energy as a function of hydrogen concentration is calculated, as well as energy barriers for hydrogen binding and release. The results confirm that graphene can be perspective material for hydrogen storage. Difference between hydrogenation of graphene, nanotubes, and bulk graphite is discussed.