Gibbs ensemble Monte Carlo simulations are undertaken in order to determine the vapor-liquid and liquid-liquid phase equilibria for mixtures containing square-well particles. Two types of binary systems are examined, namely, a mixture of hard spheres and square wells, and a symmetrical mixture of square wells in which the unlike interaction is purely repulsive, i.e., hard sphere like. The latter system exhibits liquid-liquid immiscibility as well as the usual vapor-liquid coexistence. Intermolecular potential ranges which are intermediate (lambda=1.5) and moderately long (lambda=2) are examined in order to determine the effect of range on the phase behavior. The coexistence data are also analyzed using a Wegner expansion; the differences in densities and compositions of the two coexisting phases can both be used as the order parameter. This approach enables a description of the phase equilibria over the entire fluid range. In the case of the vapor-liquid coexistence exhibited by the mixture of hard spheres and square-wells, the leading amplitude term and a universal critical exponent are sufficient to describe the coexistence curve. The same was found for pure square-well systems in an earlier paper. However, extended scaling has to be used in order to describe the liquid-liquid coexistence curves exhibited by the symmetrical square-well mixture; the first and second Wegner correction to scaling terms are used together with a universal value of the critical exponent. In contrast to what is found for the pure component systems, an increase in the range of the potential has little effect on the shapes of the coexistence curves of the mixtures, although the phase equilibria are, of course, shifted to higher temperatures. Other authors have reported a substantial system size dependence for the liquid-liquid phase equilibria of the symmetrical square-well mixture. We do not find a significant size dependence for this system, and feel that the lack of density fluctuations in the latter study are the principal cause of the effect.