A recently developed "global" renormalization group theory for calculating thermal properties of fluids both near and to far from the critical point is applied to molecules that interact via a square-well potential. Calculations of gas-liquid coexistence curve densities and vapor pressures are compared with results of recently reported Monte Carlo simulations for hard spheres that interact with square-well potentials of range 3 sigma (sigma = hard core diameter) and with both Monte Carlo and molecular dynamics simulations for square-well potential of range 1.5 sigma. Additionally, values for the effective critical point exponent beta(e) are calculated for both square wells as a function of temperature distance from the critical point.