We consider the excitation of maser emission in millimeter and submillimeter transitions of interstellar and circumstellar water. With the use of an escape probability method, we have determined the equilibrium populations in 349 rotational states of both ortho- and para-water under varying conditions of gas temperature, density, water abundance, and radiation field. Our results show that under suitable conditions, collisional excitation of warm (1000 K) interstellar gas may result in significant maser action in a total of 22 centimeter, millimeter, and submillimeter transitions of H2O. Under favorable meteorological conditions, several of these transitions might be detected from mountaintop observatories, and all of them are potentially observable from airborne altitudes. We describe the physical conditions needed to excite saturated maser action in each line, and we compute the expected emissivity when the criterion for saturation is met. We discuss the maser spectrum expected both from outflows surrounding late-type stars and from the interstellar shocks that have been proposed as the origin of 22 GHz masers in star-forming regions. We use our results to interpret the recent discoveries of maser action in the 321 GHz 10(29)-9(36) and 183 GHz 3(13)-2(20) lines of H2O, and we discuss the possibility that additional masing transitions may be detected in the future. In particular, we show that 183 GHz maser emission will almost inevitably be accompanied by maser emission in the 325 GHz 5(15)-4(22) line, a prediction which has recently motivated the search for-and discovery of-the 325 GHz water maser. Finally, we show how a comparison of maser luminosities in several lines along with future interferometric observations at millimeter and submillimeter wavelengths can serve as valuable diagnostic probes of the physical conditions in the emitting gas.