It is shown that it is now possible to include van der Waals (vdW) interactions via a nonempirical implementation of density functional (DF) theory to describe the correlation energy in electronic structure calculations on infinite systems of no particular symmetry. The vdW-DF theory [Phys. Rev. Lett. 92, 246401 (2004)] is applied to the adsorption of benzene and naphthalene on an infinite sheet of graphite, as well as the binding between two graphite sheets. A comparison with recent thermal-desorption data [Phys. Rev. B 69, 155406 (2004)] shows great promise for the vdW-DF method.