We clarify the relation between an interatomic potentials and liquid-vapor critical points. For this purpose, we calculate the liquid-vapor coexistence curves of several interatomic model potentials such as the Lennard-Jones n-6 (n=7-32), the Morse, and the modified Stillinger-Weber potentials by the NpT plus test particle method. From these results, we find several universal properties irrespective of the potential type: (1) The law of rectilinear diameter is fulfilled in the density-temperature plane. (2) The coexistence curve scaled by the critical temperature and density almost coincides with one another. On the other hand, we also find some properties which are definitely potential dependent. In order to demonstrate this point, we introduce a new parameter a(1)=2 pi /3 integral (infinity)(xmin) x du(x)/dx x(2) dx [x: reduced distance, x(min): the minimum position of a potential, u(x): reduced potential] which expresses the effect of the attractive force. By making use of this parameter, we find that the critical temperature T-c and pressure p(c) change linearly to a(1). This means that the wider the attractive part of the potential is, the higher T-c and p(c) are. In this way, we have discovered a method to estimate the critical point from microscopic information concerning interatomic potentials.