Subpicosecond fluorescence anisotropy measurements are used to characterize the rotational dynamics of coumarin 153 (C153) in 35 common solvents and eight solvent mixtures at room temperature. The rotational anisotropy decays of C153 are generally nonexponential as a result of the non-Markovian nature of the friction on its rotational motion. Rotational correlation times are observed to be larger in polar solvents than in nonpolar solvents of the same viscosity. This difference is examined in the context of theories of dielectric friction, which relate the extra friction in polar solute/solvent systems to long-range dipole-dipole interactions. Since the latter interactions have been thoroughly characterized via dynamic Stokes shift measurements for the same solute/solvent combinations studied here, the present data provide a unique opportunity to test general concepts of dielectric friction. Contrary to expectations, the departures from simple hydrodynamic behavior cannot be modeled using only theories of rotational dielectric friction. More important than dielectric friction is the role that the relative solute/solvent size plays in determining the extent of solute-solvent coupling. Once this size dependence is approximately accounted for, the remaining departures from simple hydrodynamic behavior are relatively small in all solvents. In polar aprotic solvents, solvation data indicate that dielectric friction effects should be rather modest (10-20% of the total friction). In these solvents no clear correlation is found between dielectric friction predictions and the observed solute-solvent coupling. However, in normal alcohol solvents the effects of dielectric friction are predicted to be large and well beyond the scatter in the experimental data. No evidence for such an important dielectric friction contribution is observed in these solvents, in spite of the fact that long-time components of the solvation dynamics do appear to be present in the rotational friction.