The adsorption of oxygen atoms [O(P-3)] on both ideal and hydrated rutile TiO2(110) surfaces is investigated by periodic density functional theory (DFT) calculations within the revised Perdew-Burke-Ernzerhof (RPBE) generalized gradient approximation and a four Ti-layer slab, with (2 x 1) and (3 x 1) surface unit cells. It is shown that upon adsorption on the TiO2 surface the spin of the O atom is completely lost, leading to stable surface peroxide species on both in-plane and bridging oxygen sites with O-binding energies of about 1.0-1.5 eV, rather than to the kinetically unstable terminal Ti-O and terminal O-O species with smaller binding energies of 0.1-0.7 eV. Changes in O-atom coverage ratios between 1/3 and 1 molecular layer (ML) and coadsorption of H2O have only minor effects on the O-binding energies of the stable peroxide configurations. High O-atom diffusion barriers of about 1 eV are found, suggesting a slow recombination rate of adsorbed O atoms on TiO2(110). Our results suggest that the TiOOTi peroxide intermediate experimentally observed in photoelectrolysis of water should be interpreted as a single spinless O adatom on TiO2 surface rather than as two Ti-O-. radicals coupled together.