The van der Waals potential of a neutral atom moving near a surface has both real and imaginary parts. The imaginary part corresponds to real excitations of the atom and of the surface. Because of this imaginary part, the van der Waals potential can give rise to inelastic processes in atom-surface scattering, for example excitation of electron-hole pairs or surface plasmons. Using a self-energy formulation of the complex van der Waals interaction we derive expressions for inelastic scattering probabilities of atoms or ions reflected from surfaces. In the case of ion or electron scattering from surfaces this reproduces a well-known result. We calculate the probabilities for inelastic scattering of neutral xenon atoms incident on metal surfaces at hyperthermal energies. A comparison of our results with the recent experimental measurements of electron-hole pair excitation for hyperthermal xenon scattering by Amirav and Cardillo shows that this long-range van der Waals coupling is only a small contribution to the total electron-hole pair excitation probability, which is mostly due to thermal excitation.