Molecular simulation results for the solid-liquid coexistence properties of untruncated, truncated, truncated and shifted, and truncated and shifted-force 12-6 Lennard-Jones potentials are reported. It is found that solid-liquid coexistence properties vary systematically with potential truncations, shifts, and cut-off values. Potential truncations and shifts have important consequences at low temperatures, particularly in the vicinity of the triple point. The main influence is on the coexistence pressure whereas both liquid and solid densities are less sensitive to the truncations and shifts. The data reported in this work indicate that the cut-off radius mainly affects the properties of the liquid phase whereas its influence on the solid phase is almost negligible. The data suggest a monotonic variation of the melting temperature as a function of cut-off radius, which contradicts the oscillatory behavior of the melting temperature reported elsewhere.