The statistics of intense energy dissipation events in wall-bounded shear flows are studied using highly resolved direct numerical simulations of turbulent channel flow at three different friction Reynolds numbers. Distributions of the energy dissipation rate and local dissipation scales are computed at various distances from the channel walls, with an emphasis on the behavior of the statistics in the near-wall region. The dependence of characteristic mean and local dissipation scales on wall distance is also examined over the full channel height. Systematic variations in these statistics are found close to the walls due to the anisotropy generated by mean shear and coherent vortical structures. Results near the channel centerline are consistent with those found in homogeneous isotropic turbulence.