The principle of corresponding states is re-examined in the light of recent experimental and theoretical fluid equation of state data compilations. The results are used to critically test and extend the fundamental concept of corresponding states scaling for simple fluids (including rare gases, diatomics and methane). Classical corresponding states scaling based on critical point constants is found to produce weaker universal behavior than a new scaling procedure linked directly to the two intermolecular interaction potential parameters of a Lennard-Jones-6-12 fluid. The improved universal behavior revealed using this Lennard-Jones-corresponding-states scaling may either reflect inaccuracies in previous critical constant estimates, or perhaps point to more fundamental differences between the critical properties of different fluids.