Current noise in nanoscale systems provides additional information beyond the electronic conductance. We report measurements at room temperature of the nonequilibrium "excess" noise in ensembles of atomic-scale gold junctions repeatedly formed and broken between a tip and a film, as a function of bias conditions. We observe suppression of the noise near conductances associated with conductance quantization in such junctions, as expected from the finite temperature theory of shot noise in the limit of few quantum channels. In higher conductance junctions, the Fano factor of the noise approaches 1/3 the value seen in the low conductance tunneling limit, consistent with theoretical expectations for the approach to the diffusive regime. At conductance values where the shot noise is comparatively suppressed, there is a residual contribution to the noise that scales quadratically with the applied bias, likely due to a flicker noise/conductance fluctuation mechanism.