Casalini and Roland [Phys. Rev. E 69, 062501 (2004); J. Non-Cryst. Solids 353, 3936 (2007)] and other authors have found that both the dielectric relaxation times and the viscosity, η, of liquids can be expressed solely as functions of the group (TV (γ)), where T is the temperature, V is the molar volume, and γ a state-independent scaling exponent. Here we report scaling exponents γ, for the viscosities of 46 compounds, including 11 ionic liquids. A generalization of this thermodynamic scaling to other transport properties, namely, the self-diffusion coefficients for ionic and molecular liquids and the electrical conductivity for ionic liquids is examined. Scaling exponents, γ, for the electrical conductivities of six ionic liquids for which viscosity data are available, are found to be quite close to those obtained from viscosities. Using the scaling exponents obtained from viscosities it was possible to correlate molar conductivity over broad ranges of temperature and pressure. However, application of the same procedures to the self-diffusion coefficients, D, of six ionic and 13 molecular liquids leads to superpositioning of poorer quality, as the scaling yields different exponents from those obtained with viscosities and, in the case of the ionic liquids, slightly different values for the anion and the cation. This situation can be improved by using the ratio (D∕T), consistent with the Stokes-Einstein relation, yielding γ values closer to those of viscosity.