Over the past few years a large number of density-functional schemes have been developed for molecular excited states, many of which have been shown to produce poor results for water. We apply the time-dependent density-functional method using hybrid and asymptotically corrected functionals to evaluate the vertical excitation energies, C-2v-relaxation energies and vibration frequencies, and dissociation pathways for up to eight singlet and six triplet excited states of water. The results are compared to experimental data as well as ab initio calculated data obtained using direct and equations-of-motion coupled-cluster techniques, as well as multireference configuration-interaction techniques. For most properties, the asymptotically corrected density-functional method produces results of comparable quality to those produced by the ab initio methods. However, the time-dependent methods produce very poor results for systems involving molecular dissociation. In fact, only the multireference approaches produce good descriptions of molecular dissociation, but in the regions of the (C-2v) minima of the potential energy surfaces single-reference techniques are found to be both more accurate and much more robust.