Molecular Dynamics (MD) simulations have been carried out to determine the self-diffusivities, D-i,D-self,D- of the pure hydrocarbons methane (C1), ethane (C2), propane (C3), and n-hexane (nC6) at various fluid densities. The MD simulations are in reasonable agreement with published experimental data. The influence of fluid density on both D-i,D-self,D- and the Maxwell-Stefan (M-S) diffusivities, D-ij, in binary C1-C2, C1-C3, C2-C3, and C1-nC6 mixtures was also investigated. The MD simulations show that the M-S diffusivities in binary fluid mixtures can be estimated with good accuracy using the Darken relation.