The properties of ices Ih, II, III, V, and VI at zero temperature and pressure are determined by computer simulation for several rigid water models (SPC/E, TIP5P, TIP4P/Ice, and TIP4P/2005). The energies of the different ices at zero temperature and pressure (relative to the ice II energy) are compared to the experimental results of Whalley [J. Chem. Phys. 81, 4087 (1984)]. TIP4P/Ice and TIP4P/2005 provide a qualitatively correct description of the relative energies of the ices at these conditions. In fact, only these two models provide the correct ordering in energies. For the SPC/E and TIP5P models, ice II is the most stable phase at zero temperature and pressure whereas for TIP4P/Ice and TIP4P/2005 ice Ih is the most stable polymorph. These results are in agreement with the relative stabilities found at higher temperatures. The solid-solid phase transitions at 0 K are determined. The predicted pressures are in good agreement with those obtained from free energy calculations.