Vapor-liquid, vapor-solid and liquid-solid coexistence lines are calculated for binary mixtures of Lennard-Jones spheres using Monte Carlo simulation and the Gibbs-Duhem integration technique. Complete phase diagrams showing equilibrium between vapor, liquid and solid phases are constructed for binary Lennard-Jones mixtures with diameter ratios ranging from σ11 /σ22 = 0.85–1.0 and attractive well-depth ratios ranging from ϵ11/ϵ22 = 0.625−1.6, at a reduced pressure P*≡Pσ/ϵ11 = 0.002. The Lorentz-Berthelot combining rules are used to calculate the cross-species interaction parameters σ12 and ϵ12. The variation in the shape of the complete phase diagrams change as a function of the diameter ratio σ11 /σ22 and well-depth ratio ϵ11 /ϵ22 is systematically explored. The phase diagrams found here resemble those found experimentally for argon-methane, iodine-sulfur, water-sodium chloride, water-silver nitrate, water-potassium nitrate, and p-dichlorobenzene-p-dibromobenzene.