Using extensive classical molecular dynamics simulations, we compute the dielectric and far-infrared spectra of nine popular water models, including polarizable and nonpolarizable ones. We analyze the dielectric spectra using a two-relaxation model that allows one to extract the characteristic time of both the main dielectric relaxation and the fast relaxation. The use of a Cole-Cole functional form permits also quantitative assessment of the absence of deviations from the Debye form of the main dielectric peak. In the THz region of the spectrum, we compute the infrared absorbance caused by molecular libration, which appears to be qualitatively different for three main groups of molecular models. The complexity of the librational band is further investigated by decomposing the spectrum into the contributions of water fractions with a different number of hydrogen-bonded neighbors.