Cavity-optomechanical cooling via radiation pressure dynamical backaction enables ground-state cooling of mechanical oscillators, provided the laser exhibits sufficiently low phase noise. In this paper, we investigate and measure the excess phase noise of widely tunable external cavity diode lasers, which have been used in a range of recent nano-optomechanical experiments, including ground-state cooling. We report significant excess frequency noise, with peak values of the order of 10(7) rad(2) Hz near 3.5 GHz, attributed to the diode lasers' relaxation oscillations. The measurements reveal that even at GHz frequencies diode lasers do not exhibit quantum-limited performance. The associated excess backaction can preclude ground-state cooling even in state-of-the-art nano-optomechanical systems and can, moreover, lead to noise-induced sideband asymmetries.