The efficacy of spatial diversity in practical free-space optical communication systems is impaired by the fading correlation among the underlying subchannels. We consider in this paper the generation of correlated Gamma-Gamma random variables in view of evaluating the system outage probability and bit-error-rate under the condition of correlated fading. Considering the case of receive-diversity systems with intensity modulation and direct detection, we propose a set of criteria for setting the correlation coefficients on the small- and large-scale fading components based on scintillation theory. We verify these criteria using wave-optics simulations and further show through Monte Carlo simulations that we can effectively neglect the correlation corresponding to the small-scale turbulence in most practical systems, irrespective of the specific turbulence conditions. This has not been clarified before, to the best of our knowledge. We then present some numerical results to illustrate the effect of fading correlation on the system performance. Our conclusions can be generalized to the cases of multiple-beam and multiple-beam multiple-aperture systems.