All surfaces in water experience at short separations hydration repulsion or hydrophobic attraction, depending on the surface polarity. These interactions dominate the more long-ranged electrostatic and van der Waals interactions and are ubiquitous in biological and colloidal systems. Despite their importance in all scenarios where the surface separation is in the nanometer range, the origin of these hydration interactions is still unclear. Using atomistic solvent-explicit molecular dynamics simulations, we analyze the interaction free energies of charge-neutral model surfaces with different elastic and water-binding properties. The surface polarity is shown to be the most important parameter that not only determines the hydration properties and thereby the water contact angle of a single surface but also the surface-surface interaction and whether two surfaces attract or repel. Elastic properties of the surfaces are less important. On the basis of surface contact angles and surface-surface binding affinities, we construct a universal interaction diagram featuring three different interaction regimes-hydration repulsion, cavitation-induced attraction-and for intermediate surface polarities-dry adhesion. On the basis of scaling arguments and perturbation theory, we establish simple combination rules that predict the interaction behavior for combinations of dissimilar surfaces.