Molecular dynamics simulations allow detailed study of the experimentally inaccessible liquid state of supercooled water below its homogeneous nucleation temperature and the characterization of the glass transition. Simple, nonpolarizable intermolecular potentials are commonly used in classical molecular dynamics simulations of water and aqueous systems due to their lower computational cost and their ability to reproduce a wide range of properties. Because the quality of these predictions varies between the potentials, the predicted glass transition of water is likely to be influenced by the choice of potential. We have thus conducted an extensive comparative investigation of various three-, four-, five-, and six-point water potentials in both the NPT and NVT ensembles. The T-g predicted from NPT simulations is strongly correlated with the temperature of minimum density, whereas the maximum in the heat capacity plot corresponds to the minimum in the thermal expansion coefficient. In the NVT ensemble, these points are instead related to the maximum in the internal pressure and the minimum of its derivative, respectively. A detailed analysis of the hydrogen-bonding properties at the glass transition reveals that the extent of hydrogen-bonds lost upon the melting of the glassy state is related to the height of the heat capacity peak and varies between water potentials.