Results are presented for the reaction of gas-phase H atoms with H atoms adsorbed onto a variety of substrates. Time-dependent quantum methods are used to compute reaction cross sections and product H-2 rotational and vibrational distributions for a large number of model potential energy surfaces. The potentials which model reactions on metals exhibit a wide range of reactivity. In addition, the single-collision Eley-Rideal reaction cross sections are generally small, suggesting that hot-atom processes should in general play an important role in H-2 formation on metal surfaces. These observations are consistent with recent experiments. Eley-Rideal reactivity is shown to increase as the strength of the H-substrate bond decreases, and H atom trapping becomes less favorable. The cross sections for the reaction of H(g) with H adsorbed onto model graphite surfaces are generally large (5-10 Angstrom (2)).