A systematic study of the self-diffusion coefficient in hard-sphere fluids, Lennard-Jones fluids, and real compounds over the entire range of gaseous and liquid states is presented. First an equation is proposed for the self-diffusion coefficient in a hard-sphere fluid based on the molecular dynamics simulations of Alder et al. (J. Chem. Phys. 1970, 53, 3813) and Erpenbeck and Wood (Phys. Rev. A 1991, 43, 4254). That expression, extended to the Lennard-Jones fluids through the effective hard-sphere diameter method, represents accurately the self-diffusion coefficients obtained in the literature by molecular dynamics simulations, as well as those determined experimentally for argon, methane, and carbon dioxide. A rough Lennard-Jones expression which contains besides the diameter sigma(LJ) and energy epsilon(LJ) the translational-rotational factor, A(D) (which could be correlated with the acentric-factor), is adopted to describe the self-diffusion in nonspherical fluids. The energy parameter is estimated using a correlation obtained from viscosity data, and the molecular diameter is obtained from the diffusion data themselves. The equation represents the self-diffusion coefficients with an average absolute deviation of 7.33%, for 26 compounds (1822 data points) over wide ranges of temperature and pressure.