The phase diagrams of systems made up of hard spheres interacting with attractive potentials of the form -1/r3+sigma are calculated using Monte Carlo simulations, second-order thermodynamic perturbation theory, and an augmented van der Waals theory. In simulations of the systems with sigma= 0.1, 1, and 3, fluid-solid coexistence results are obtained using the Gibbs-Duhem integration technique; simulation data for the vapor-liquid coexistence envelopes and critical points are taken from previously published work. It is shown that the agreement between the theoretical and simulated phase diagrams improves as the range of the potential is increased, reflecting the decreasing role of short-range correlations in determining the bulk thermodynamics. In the extreme case of sigma= 0.1 both theories are in excellent agreement with simulations. Phase diagrams for systems with sigma=4, 5, and 6 are computed using second-order thermodynamic perturbation theory. The results indicate that the vapor-liquid transition becomes metastable with respect to freezing when s*5, in broad agreement with results for the hard-sphere attractive Yukawa system which is commonly used to model colloidal particles, globular proteins, and nanoparticles.