We have studied the dependence of azimuthal anisotropy nu(2) for inclusive and identified charged hadrons in Au + Au and Cu + Cu collisions on collision energy, species, and centrality. The values of nu(2) as a function of transverse momentum pT and centrality in Au + Au collisions at root s(NN) = 200 and 62.4 GeV are the same within uncertainties. However, in Cu + Cu collisions we observe a decrease in nu(2) values as the collision energy is reduced from 200 to 62.4 GeV. The decrease is larger in the more peripheral collisions. By examining both Au + Au and Cu + Cu collisions we find that nu(2) depends both on eccentricity and the number of participants, N-part. We observe that nu(2) divided by eccentricity (epsilon) monotonically increases with N-part and scales as N-part(1/3). The Cu + Cu data at 62.4 GeV falls below the other scaled nu(2) data. For identified hadrons, nu(2) divided by the number of constituent quarks n(q) is independent of hadron species as a function of transverse kinetic energy K E-T = m(T) - m between 0.1 < K E-T / n(q) < 1 GeV. Combining all of the above scaling and normalizations, we observe a near-universal scaling, with the exception of the Cu + Cu data at 62.4 GeV, of nu(2)/(nq center dot e center dot N-part(1/3)) vs K E-T / n(q) for all measured particles.