The radiation damping rate of plasmon resonances in pairs of spherical gold nanoparticles is calculated. The radiative line width of the plasmon resonance indicates significant far-field coupling between the nanoparticles over distances many times the particle diameter. The radiation damping of the coupled particle-plasmon mode alternates between superradiant and subradiant behavior when the particle spacing is varied. At small particle spacings where near-field coupling occurs, the radiation damping rate lies far below that of an isolated particle.