Efficient on-board hydrogen storage for fuel cell vehicles is one of the most vexing problems associated with the use of hydrogen as a transportation energy carrier. Hydrides of light metals can have both high gravimetric and volumetric hydrogen densities, making them good candidates for mobile storage technologies. One of the main problems associated with metal hydrides is unfavorable thermodynamics, meaning that unacceptably high temperatures are required to release the hydrogen. The kinetics of hydrogen release and uptake (for refueling) is also a major consideration, but thermodynamics is the primary consideration when screening new hydride materials. We present predictions for the thermodynamics of a very large number of metal hydrides that have reasonably high gravimetric hydrogen densities based on calculations from ab initio density functional theory. We examine both the lowest energy (convex hull) reaction pathways as well as metastable pathways that lie within 10 kJ/mol of the convex hull. We also consider multistep reactions. We use a thermodynamic grand potential approach to identify reactions that lie on the convex hull.