During our recent simulation studies of the contact values of the density and charge profiles formed by symmetric and asymmetric electrolytes near charged electrodes, we have accumulated a large number of Monte Carlo (MC) simulation results for ionic distribution profiles as a function of the distance of the ions from the electrode. The ions were modeled as charged hard spheres in a dielectric continuum whose dielectric constant equals that of the solvent (the primitive model), while the electrode was modeled as a hard unpolarized uniformly charged planar surface. Some of the density and potential profiles for this model system for electrolytes with one or both asymmetric in charge and size for varying electrolyte concentrations and electrode charge densities are reported here. These simulations are used to assess the results of (i) the classical Poisson-Boltzmann (PB) theory, (ii) a simplified extension of the Poisson-Boltzmann theory, called PB+EVT, that includes excluded volume effects but neglects ion correlations beyond those provided by the charge interactions, and (iii) in the case of charge asymmetry but symmetric size, the modified Poisson-Boltzmann (MPB) theory. The PB results are rather poor, whereas the MPB results are quite good. At low concentrations, the PB+EVT results are nearly the same as the PB results. However, some improvement is seen at higher concentrations.