A state of random close packing (RCP) of spheres is found to have a thermodynamic status and a fundamental role in the description of liquid-state equilibria. The RCP limiting amorphous ground state, with reproducible density and well-characterized structure, is obtained by well-defined irreversible and reversible processes. The limiting packing fraction y(RCP) = 0.6366 +/- 0.0005 (Buffon's constant within the uncertainty), and a residual entropy per sphere Delta S(RCP-FCC) similar or equal to k(B) (Boltzmann's constant). Since the Mayer virial expansion does not represent dense fluid equations-of-state for densities exceeding the available-volume percolation transition (rho(pa)), we infer that a RCP state belongs to the same thermodynamic phase as prepercolation equilibrium dense hard-sphere fluid and likewise for hard-core fluids with attractive forces. Monte Carlo (MC) calculation of the liquid-state coexistence properties of square-well (SW) attractive spheres, together with existing MC results for liquid-vapor coexistence in the SW fluid, support this conclusion. Further findings for liquid-vapor coexistence limits are reported. The extremely weak second-order available-volume percolation transition of the hard-sphere fluid is strengthened by square-well perturbation as temperature is reduced. At the critical temperature, this transition becomes first order, whereupon a liquid at the percolation density coexists in thermodynamic equilibrium with its vapor at a lower density. The critical coexisting vapor density relates to the extended-volume bonded cluster percolation transition rho(pe)(lambda) defined for given well width (lambda). Taking experimental liquid argon data as an example, it can be seen that the thermodynamic description of the coexistence limits, found here for square-well fluids, applies to real liquids.