We present STAR measurements of the azimuthal anisotropy parameter v_2 for pions, kaons, protons, Lambda, bar Lambda, Xi+bar Xi, and \Omega + bar Omega, along with v_4 for pions, kaons, protons, and Lambda + bar Lambda at mid-rapidity for Au+Au collisions at sqrt sNN=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 percent-15 percent larger than those in Pb+Pb collisions at sqrt s NN =17.3 GeV. At intermediate transverse momentum (p_T from 1.5-5 GeV/c), the 62.4 GeV v_2(p_T) and v_4(p_T) values are consistent with the quark-number scaling first observed at 200 GeV. A four-particle cumulant analysis is used to assess the non-flow contributions to pions and protons and some indications are found for a smaller non-flow contribution to protons than pions. Baryon v_2 is larger than anti-baryon v_2 at 62.4 and 200 GeV perhaps indicating either that the initial spatial net-baryon distribution is anisotropic, that the mechanism leading to transport of baryon number from beam- to mid-rapidity enhances v_2, or that anti-baryon and baryon annihilation is larger in the in-plane direction.