First principles calculations were systematically performed for 31 binary metal-hydrogen (M-H) systems on a set of 30 potential crystal structures selected on the basis of experimental data and possible interstitial sites. For each M-H system, the calculated enthalpies of formation were represented as functions of H composition. The zero point energy correction was considered for the most stable hydrides via additional harmonic phonon calculations. The sequence of stable hydrides (ground-state) given by the convex hull was found in satisfactory agreement with the experimental data. Besides, new high pressure dihydrides and trihydrides were predicted, providing orientations for new materials synthesis. The overall results provide a global overview of hydride relative stabilities and relevant input data for thermodynamic modeling methods.