We studied the interaction of perfect and lightly reduced ceria (111) surfaces with hydrogen and water molecules using density functional calculations implementing the generalized gradient approximation (GGA) and onsite Coulomb interactions (GGA+U). We predicted the relative surface energies at different states of reduction and in the presence of water, allowing insight into surface processes under a variety of conditions. Several unusual properties of the ceria surface were brought to the fore: the dissociation of water molecules on the ideal surface, the rapid dissociation of water at vacancy sites, and the strongly exothermic dissociation of H-2 on the ideal surface. These results have strong implications for the interpretation of experimental data and the construction of reaction schemes for this technologically important metal oxide surface.