We examine the momentum and energy dependence of the scattering rate of the high-temperature cuprate superconductors using angle-resolved photoemission spectroscopy. The scattering rate is of the form a+bw around the Fermi surface for under-and optimal doping. The inelastic coefficient b is found to be isotropic. The elastic term a, however, is found to be highly anisotropic for under-and optimally doped samples, with an anisotropy which correlates with that of the pseudogap. This is contrasted with heavily overdoped samples, which show an isotropic scattering rate and an absence of the pseudogap above T-c. We find this to be a generic property for both single-and double-layer compounds.