The long-time decay of the shear-stress autocorrelation function is shown to be quantitatively related to the decay of correlations between the orientation of "bonds" connecting colliding pairs of particles. Within computational uncertainties, we find that orientational correlations in high-density fluids decay as a "stretched" exponential in time, with an exponent that is independent of density. However, at low densities the decay is exponential. In two-dimensional systems the decay is exponential, even at high density.