A predictive scheme of viscosity for pure fluids and mixtures of simple molecules is presented. First, using molecular dynamics data from the literature and also from our own study, a representative correlation of the viscosity of a Lennard-Jones fluid is developed for a wide range of thermodynamic states. Second, a corresponding states scheme is proposed which allows the transposition of the previous results to real fluids. For some simple molecules, this scheme induces deviations lower than 5% in conditions covering gas, liquid, and supercritical states. For larger molecules, the results are poorer but can be strongly improved by fitting the atomic diameter. Then, it is shown for simple binary and multicomponent mixtures that, by using merely a van der Waals one-fluid approximation and the Lorentz - Berthelot rules, results are as good as for pure fluids. Finally, the limitations of such a scheme are shown when applied on the methane + toluene asymmetric mixture.