The results for cluster shape anisotropy over a broad range (10(-3)-10(-1)) of monomer volume fractions, f(v) values, are presented for both two- (2d) and three-dimensional (3d) simulations of diffusion-limited (DLCA), ballistic-limited (BLCA), and reaction-limited (RLCA) cluster-cluster aggregation classes. We find that all three aggregation classes have different dilute-limit shape anisotropies, with the diffusion-limited model having the largest value of anisotropy and the reaction-limited model having the smallest. The simulation result for the cluster shape anisotropy for each of the three aggregation classes is slightly less than the corresponding prediction of the hierarchial model. In addition, we find excellent agreement between the 2d DLCA simulation results and experimental measurements of shape anisotropy. At late times, shape anisotropy decreases from the dilute-limit value.