In the three nearest luminous galaxies, the Milky Way System, the Andromeda Galaxy, and NGC 5128, the brightest globular clusters are rounder than the faintest ones. On the other hand (contrary to some previous results) the flattening of individual Large Magellanic Cloud clusters is found to be independent of their luminosities. This suggests the possibility that the relationship between the flattening and luminosity of clusters might depend on host galaxy luminosity. No significant differences are found between the intrinsic flattening distributions of Galactic old halo, Galactic young halo, and Galactic bulge/disk clusters. Such a dependence might perhaps have been expected if tidal forces (which are largest at small Galactocentric distances) removed angular momentum from globular clusters. The preliminary conclusion by Norris that clusters with blue horizontal branches are more flattened than red horizontal-branch (HB) clusters is not confirmed by the larger database that is now available. In other words there is no evidence for the puzzling claimed correlation between the flattening and the horizontal branch morphology of Galactic globular clusters.