New measurements are presented for charged hadron azimuthal correlations at midrapidity in Au+Au collisions at root s(NN)=62.4 and 200 GeV. They are compared to earlier measurements obtained at root s(NN)=130 GeV and in Pb+Pb collisions at root s(NN)=17.2 GeV. Sizeable anisotropies are observed with centrality and transverse momentum (p(T)) dependence characteristic of elliptic flow (v(2)). For a broad range of centralities, the observed magnitudes and trends of the differential anisotropy, v(2)(p(T)), change very little over the collision energy range root s(NN)=62-200 GeV, indicating saturation of the excitation function for v(2) at these energies. Such a saturation may be indicative of the dominance of a very soft equation of state for root s(NN)similar to 60-200 GeV.