The ubiquitous van der Waals (vdW) force, particularly discernible in weak adsorption, is studied on noble and transition metals. In calculations with the vdW density functional (DF) [M. Dion et al., Phys. Rev. Lett. 92, 246401 (2004)], the atomic structure near the adsorption site is systematically varied, including dense fcc(111) surface, adatom, pyramid, and step defects. In weak adsorption the vdW force (i) is shown necessary to account for, (ii) is sizable, (iii) has a strong spatial variation, relevant for adsorption on surface defects, (iv) changes reaction rules, and (v) changes adsorption trends in agreement with experimental data. Traditional physisorption theory is also given support and interpretation.