One of the most fundamental properties of both Newton's mechanics and Maxwell electrodynamics is the absence of any physical constants in their basic equations. All necessary constants appear only at the stage of applications of these theories to specific phenomena. This is one of the reasons of universality and generality of these theories since physical constants always reflect our ignorance in formulation of physical laws. Therefore primary equations of physics should not contain physical constants at all, including the fundamental ones.
Quantum mechanics and general relativity seem to be counterexamples of the above requirement since Schroedinger equation contains both the fundamental Planck constant and the mass of the particle and Einstein equation contains the gravitational constant. It is however possible to suspect that both these great theories may be in some sense secondary and their basic equations may be derived from more fundamental formulations in which all physical constants do not appear.