Hartree-Fock calculations for spherical nuclei using Skyrme's density-dependent effective nucleon-nucleon interaction are discussed systematically. Skyrme's interaction is described and the general formula for the mean energy of a spherical nucleus derived. Hartree-Fock equations are obtained by varying the mean energy with respect to the single-particle wave functions of occupied states. Relations between the parameters of the Skyrme force and various general properties of nuclear matter and finite nuclei are analyzed. Calculations have been made for closed-shell nuclei using two rather different sets of parameters, both of which give good binding energies and radii for 16O and 208Pb. Both interactions give good binding energies and charge radii for all closed-shell nuclei. Calculated electron scattering angular distributions agree qualitatively with experiment, and for one interaction there is good quantitative agreement. The single-particle energies calculated with the two interactions are somewhat different owing to a different nonlocality of the Hartree-Fock potentials, but both interactions give the correct order and density of single-particle levels near the Fermi level. They differ most strongly in their predictions for the energies of 1s single-particle states.