Top quark pair production by (polarized) gg collisions offers an interesting testing ground of the Standard Model and its extensions. In this Letter we present results for differential cross sections of top quark pair production and decay including QCD radiative corrections. We take into account the full dependence on the top quark spins. We give analytic and numerical results for single and double differential angular distributions of tt decay products which are due to top quark polarizations and spin correlations in the intermediate state.