The adiabatic-connection fluctuation-dissipation theorem suggests that the correlation energy in the random phase approximation is a suitable complement to exact exchange. We show that lattice constants, bulk moduli, and atomization energies of solids evaluated using this approximation are in very good agreement with experiment. Since the method is fairly efficient and handles ionic, metallic, and van der Waals bonded systems equally well, it is a very promising choice to improve upon density functional theory calculations, without resorting to more demanding diffusion Monte Carlo or quantum chemical methods.