The phase diagram of water as obtained from computer simulations is presented for the first time for two of the most popular models of water, TIP4P and SPC/E. This Letter shows that the prediction of the phase diagram is an extremely stringent test for any water potential function, and that it may be useful in developing improved potentials. The TIP4P model provides a qualitatively correct description of the phase diagram, unlike the SPC/E model which fails in this purpose. New behavior not yet observed experimentally is predicted by the simulations: the existence of metastable reentrant behavior in the melting curves of the low density ices (I,III,V) such that it could be possible to transform them into amorphous phases by adequate changes in pressure.