The standard approximation in continuum electrostatic theory, that polar liquids respond linearly to changes in electric fields, is examined on a microscopic level by molecular dynamics and thermodynamic perturbation simulations. Electrostatic free energies associated with the process of "charging" a solute in a solvent are evaluated and compared to the predictions from linear response, fur a number of compounds. it is found that the linear response approximation generally holds well for monovalent ionic solutes, while it is less accurate for dipolar ones. Deviations observed for dipolar compounds are reflected by unequal curvatures of the free energy functions (potentials of mean force) near their respective minima for the "polar" and "nonpolar stales". The short-range nature of dipolar fields gives relatively larger weight to the innermost solvation shells in determining the electrostatic part of the solvation energy, compared to the case of ionic solutes, These inner shells call exhibit nonlinear response due to saturation and/or disruption of the H-bond network (in protic solvents) near the solute. This nonlinearity appears to reach a maximum when the strengths of solute-solvent and solvent-solvent interactions are matched. We also find that the average potential produced by solvent water is negative for an uncharged van der Waals cavity. While this has no bearing on the validity of linear response, it affects the magnitude of the hydration energy for certain ions, Relationships between solvation energies and average interaction energies, derived in this work, can be useful for simplified free energy calculations and their applications to drug design.