Van der Waals (dispersion) forces contribute to interactions of proteins with other molecules or with surfaces, but because of the structural complexity of protein molecules, the magnitude of these effects is usually estimated based on idealized models of the molecular geometry, e.g., spheres or spheroids. The calculations reported here seek to account for both the geometric irregularity of protein molecules and the material properties of the interacting media. Whereas the latter are found to fall in the generally accepted range, the molecular shape is shown to cause the magnitudes of the interactions to differ significantly from those calculated using idealized models, with important consequences. First, the roughness of the molecular surface leads to much lower average interaction energies for both protein-protein and protein-surface cases relative to calculations in which the protein molecule is approximated as a sphere. These results indicate that a form of steric stabilization may be an important effect in protein solutions. Underlying this behavior is appreciable orientational dependence, one reflection of which is that molecules of complementary shape are found to exhibit very strong attractive dispersion interactions. Although this has been widely discussed previously in the context of molecular recognition processes, the broader implications of these phenomena may also be important at larger molecular separations, e.g., in the dynamics of aggregation, precipitation, and crystal growth.