The dielectric properties (static dielectric constant epsilon(0), Debye relaxation time tau(D) and distance dependent Kirkwood G-factor G(k)(R)) of commonly used three-site water models (the "simple point charge" models SPC and SPC/E, as well as the "transferable intermolecular potentials with three point charges" TIP3P and its CHARMM modified variant TTP3P(mod)) were evaluated from 2 ns molecular dynamics simulations using the Ewald summation method to compute the electrostatic interactions. The results for SPC (epsilon(0) = 65 +/- 5, tau(D) = 7.6 +/- 0.8 ps) and SPC/E (epsilon(0) = 68 +/- 6, tau(D) = 12.1 +/- 1.3 ps) are in good agreement with the literature; for TIP3P (TIP3P(mod)) we obtained a dielectric constant epsilon(0) = 97 +/- 7 (97 +/- 6) and a Debye relaxation time tau(D) = 7.3 +/- 0.7 ps (6.9 +/- 0.6 ps). The surprisingly large differences in Eo were rationalized by an investigation of the relationship between the force field parameters and the dielectric properties. Based on simulations of hybrid SPC/TIP3P models, the HOH bond angle was identified as the determining factor of the dielectric constant. By contrast, tau(D) was shown to depend mainly on the OH bond length and the partial charges; the HOH angle is of secondary importance. The role of the HOH angle is clarified by a comparison of the orientational correlation functions of the water models.