A hybrid equation of state for the Helmholtz energy F of Stockmayer fluids is constructed as the sum of the Helmholtz energy F-LJ for the Lennard-Jones fluid and the dipolar contribution to the Helmholtz energy F-D, F = F-LJ + F-D. Predictions from this equation for the thermodynamic properties of the homogeneous phases and for the vapour-liquid phase equilibria show good to excellent agreement with simulation data. Moreover, the properties of mixtures of Stockmayer with Lennard-Jones molecules are shown to be well predicted by using an appropriate mixing rule. For these mixtures, also liquid-liquid phase separations and vapour-liquid phase equilibria are calculated.