Direct simulations of large populations of confined hydrodynamically interacting swimming particles at low Reynolds number are performed. Hydrodynamic coupling between the swimmers leads to large-scale coherent vortex motions in the flow and regimes of anomalous diffusion that are consistent with experimental observations. At low concentrations, swimmers propelled from behind (like spermatazoa) strongly migrate toward solid surfaces in agreement with simple theoretical considerations; at higher concentrations this localization is disrupted by the large-scale coherent motions.