Periodic-density functional theory (DFT) and Hartree-Fock calculations have been performed on the alkali halides for the alkali metals Li, Na, K, and Rb and the halogens F, Cl, Br and I. Calculations were done with HF-optimized basis sets and DFT-optimized basis sets, at the HF, local DFT (LDFT), and nonlocal DFT (NLDFT) with the Becke exchange potential and the Perdew-Wang correlation potential. The HF and NLDFT results are similar for the lattice parameters, in general, by overestimating them. The LDFT method always underestimates the lattice parameters. As a consequence, the HF and NLDFT methods predict bulk moduli that are too small and the LDFT method predicts bulk moduli that are too large. The absolute error in the bulk moduli are larger at the LDFT level than at the other levels. Charge distribution maps have been calculated and analyzed. The maps clearly show that the main difference between the HF and DFT densities is in the treatment of exchange and that the nonlocal (gradient) corrections moderate this difference.