We develop a crossover equation of state (EOS) for square-well fluids with varying well width. This equation yields the exact second and third virial coefficients, and accurately reproduces first-order (high-temperature) perturbation theory results. In addition, this EOS yields the correct scaling exponents near the critical point. We perform extensive new molecular dynamics and Monte Carlo simulations in the one-phase region for varying well widths of lambda = 1.5, 2.0, and 3.0. We fit the parameters of our EOS to one-phase and two-phase thermodynamic data from our simulations and those of previous researchers. The resulting EOS is found to represent the thermodynamic properties of these square-well fluids to less than 1% deviation in internal energy and density and 0.1% deviation in vapor pressure.