This paper describes results of simulations of solvation dynamics of a variety of solutes in two reference solvents, acetonitrile and methanol. Part of these studies involve attempts to realistically model the solvation dynamics observed experimentally with the fluorescence probe coumarin 153 (C153). After showing that linear response simulations afford a reliable route to the dynamics of interest, experimental and simulation results for C153 are compared. Agreement between the observed and calculated dynamics is found to be satisfactory in the case of acetonitrile but poor in the case of methanol. The latter failure is traced to a lack of realism in the dielectric properties of the methanol model employed. A number of further simulations are then reported for solvation of a number of atomic, diatomic, and benzenelike solutes which are used to elucidate what features of the solute are important for determining the time dependence of the solvation response. As far as large polyatomic solutes like C153 are concerned, the solute attribute of foremost importance is shown to be the "effective moment" of its charge distribution (actually the difference between the S-1 and S-0 charge distributions). This effective moment, determined from consideration of continuum electrostatics, provides a simple measure of how rapidly the solute’s electric field varies spatially in the important regions of the solvent. Simulations of fictitious excitations in a benzene solute show that this single quantity is able to correlate the dynamics observed in widely different solutes. Also explored is the effect of solute motion on its solvation dynamics. While of minor relevance for large solutes like C153, in small solutes of the size of benzene, solute motion can dramatically enhance the rate of solvation. A model based on independent solvent dynamics and solute rotational motion is able to account for the bulk of the observed effects. Finally, the influence of solute polarizability on solvation dynamics is considered. Simulations of diatomic molecules with a classical polarizability show that the rate of solvation decreases roughly in proportion to the polarizability of the solute. This dynamical effect can be understood in terms of the change that polarizability produces on the solvation force constant. These simulations indicate that the magnitude of the effect should be relatively small (10%-25%) in real systems, at least in the linear response limit.