We report granular temperature data and long-time dynamics of mono-disperse glass particles in a three-dimensional dense bed subject to vertical sinusoidal vibrations over a wide range of conditions. The granular temperature of the particles was found to scale with the square of the peak vibrational velocity. The mean time of flight between the collisions was found to scale with the inverse of the square of the peak vibrational velocity, whilst the mean free path of the particles was observed to scale with the inverse of this velocity. The movement of the particles throughout the bed, which was observed to be sub-diffusive over macroscopic timescales for all conditions considered here, appears to be governed by collective motion of particles between cavities defined by their neighbours. (C) 2007 Elsevier B.V. All rights reserved.