Introduction of economically viable hydrogen cars is hindered by the need to store large amounts of hydrogen. Metal borohydrides [LiBH4, mg(BH4)(2), Ca(BH4)(2)] are attractive candidates for onboard storage because they contain high densities of hydrogen by weight and by volume. Using a set of recently developed theoretical first-principles methods, we predict currently unknown crystal structures and hydrogen storage reactions in the Li-Mg-Ca-B-H system. Hydrogen release from LiBH4 and Mg(BH4)(2) is predicted to proceed via intermediate Li2B12H12 and MgB12H12 phases, while for Ca borohydride two competing reaction pathways (into CaB6 and CaH2, and into CaB12H12 and CaH2) are found to have nearly equal free energies. We predict two new hydrogen storage reactions that are some of the most attractive among the presently known ones. They combine high gravimetric densities (8.4 and 7.7 wt % H-2) with low enthalpies [approximately 25 kJ/(mol H-2)] and are thermodynamically reversible at low pressures due to low vibrational entropies of the product phases containing the [B12H12](2-) anion.