The phase diagrams of hard-core Yukawa mixtures (HCYM), constituted of equal sized hard spheres interacting through an attractive Yukawa tail, are determined by means of Gibbs Ensemble Monte Carlo (GEMC) simulations, Semi-grand Canonical Monte Carlo (SGCMC) simulations, and through the modified hypernetted-chain (MHNC) theory. Freezing lines are obtained according to an approach recently proposed by Giaquinta and co-workers [Physica A 187, 145 (1992); Phys Rev. A 45, 6966 (1992)] in which an analysis of multiparticle contributions to the excess entropy, Delta s, is performed, with the determination of the Delta s=0 locus. Liquid-vapor coexistence, determined through GEMC simulations, turns out to be favored when the strength ratio nu of unlike to like particle interaction, is close to 1. For lower nu＇s, liquid-vapor coexistence is favored at low densities, and Liquid-liquid coexistence, determined through SGCMC simulations, at high densities. The liquid-vapor binodal shifts downward in temperature and flattens when nu decreases, with a decrease of the critical temperature. At nu=0.9 a triple point can be identified from the intersection of the freezing Line with the binodal line; at nu=0.7, instead, the binodal ends on the line of liquid-liquid (consolute) critical points, the intersection of the two lines thus identifying the ＇＇crossover＇＇ density and temperature between the two equilibrium regimes which correspond to the critical end point of the mixture. We find that, for not too high densities, consolute equilibrium can be also explored through GEMC simulations; the results for liquid-liquid coexistence obtained through this method and SGCMC simulations compare quite satisfactorily with each other. The trend of the liquid-vapor binodal to disappear for relatively weak unlike interactions is discussed in connection with the disappearance of liquid-vapor equilibrium which occurs in one component hard-core Yukawa fluids characterized by very short ranged attractive forces. The latter behavior has been conjectured to be relevant for the onset of crystallization in protein solutions; the implications of the present results, which are obtained in the context of a two component, albeit rough, modelization of a realistic solution, are discussed. In agreement with similar results obtained by Giaquinta et al., we finally find that the Delta s=0 locus not only brings the signature of the freezing transition, but also of structural rearrangements preluding to other phase equilibria; in fact, the Delta s=0 line turns out to be coincident to a high accuracy with the line of consolute critical points and with the gas branches of the Liquid-vapor binodals.