We present an analysis of the morphology of the water dimer potential energy surface (PES) obtained from ab initio electronic structure calculations and perform a quantitative comparison with the results from various water potentials. In order to characterize the morphology of the PES we have obtained minimum energy paths (MEPs) as a function of the intermolecular O-O separation by performing constrained optimizations under various symmetries (C-s, C-i, C-2, and C-2v). These constitute a primitive map of the dimer PES and aid in providing an account for some of its salient features such as the energetic stabilization of "doubly hydrogen-bonded" configurations for R(O-O)<2.66 &ANGS;. Among the various interaction potentials that are examined, it is found that the family of anisotropic site potential (ASP) models agrees better with the ab initio results in reproducing the geometries along the symmetry-constrained MEPs. It is demonstrated that the models that produce closest agreement with the morphology of the ab initio PES, tend to better reproduce the experimental data for the second virial coefficients. We finally comment on the functional forms of simple water models and discuss how effects such as charge overlap can be incorporated into such models.