Elastic and dissipative properties of granular assemblies under uniaxial compression are studied both experimentally and by numerical simulations. Following a novel compaction procedure at varying oscillatory pressures, the stress response to a step strain reveals an exponential relaxation followed by a slow logarithmic decay. Simulations indicate that the latter arises from the coupling between damping and collective grain motion predominantly through sliding. We characterize an analogous "glass transition" for packed grains, below which the system shows aging in time-dependent sliding correlation functions.