A density-functional theory study of van der Waals forces on rare-gas diatomics is carried out. Hartree-Fock-Kohn-Sham formalism is used, that is, the exchange-correlation functional is expressed as the combination of Hartree-Fock exchange plus an approximation to the correlation energy functional. Spectroscopic constants (R-e, omega(e), and D-e) and potential energy curves for the molecules He-2, Ne-2,Ar-2, HeNe, HeAr, and NeAr are presented. Several approximations to the correlation functional are tested. The best results, in good agreement with reference experimental data, are obtained with the functional proposed by Wilson and Levy [L. C. Wilson and M. Levy, Phys. Rev. B 41, 12930 (1990)].