We present STAR measurements of the azimuthal anisotropy parameter v(2) for pions, kaons, protons, Lambda,(Lambda) over bar,Xi+ (Xi) over bar, and Omega+ (Omega) over bar, along with v(4) for pions, kaons, protons, and Lambda+(Lambda) over bar at midrapidity for Au+Au collisions at root s(NN)=62.4 and 200 GeV. The v(2)(p(T)) values for all hadron species at 62.4 GeV are similar to those observed in 130 and 200 GeV collisions. For observed kinematic ranges, v(2) values at 62.4, 130, and 200 GeV are as little as 10-15% larger than those in Pb+Pb collisions at root s(NN)=17.3 GeV. At intermediate...