Molecular dynamics simulations of five water models, the TIP3P (original and modified), SPC (original and refined), and SPC/E (original), were performed using the CHARMM molecular mechanics program. All simulations were carried out in the microcanonical NVE ensemble, using 901 water molecules in a cubic simulation cell furnished with periodic boundary conditions at 298 K. The SHAKE algorithm was used to keep water molecules rigid. Nanosecond trajectories were calculated with all water models for high statistical accuracy. The characteristic self-diffusion coefficients D and radial distribution functions, g_OO, g_OH, and g_HH for all five water models were determined and compared to experimental data. The effects of velocity rescaling on the self-diffusion coefficient D were examined. All these empirical water models used in this study are similar by having three interaction sites, but the small differences in their pair potentials composed of Lennard-Jones (LJ) and Coulombic terms give significant differences in the calculated self-diffusion coefficients, and in the height of the second peak of the radial distribution function g_OO.