Linear cavity solvation models predict saturation of the solvation chemical potential, mu(p) --> constant, at high solvent polarity. This qualitative prediction is tested on computer simulations of dipole solvation in dipolar hard-sphere solvents in the liquid and solid phase states. We find that solvation saturation does exist for solid dipolar solvents, but does not exist for liquid dipolar solvents when the linear solvent response holds. Solvation saturation occurs due to nonlinear solvation in liquid solvents when solvent-solvent attractions exceed solute-solvent attractions. Nonlinear solvation is caused by electrostriction resulting in dewetting of the solute surface of a nonpolar or weakly polar dipolar solute. Solvation thermodynamics is affected by a combination of orientational and density solvent reorganization. The relative contribution of each component is strongly dependent on solvent polarity. In highly polar solvents, the orientational and density reorganization approximately equally contribute to the average solvation energy and the second solvation cumulant. The entropy of solvation is found to be positive and virtually independent of solvent polarity. This conics about as a result of a compensation between a negative solvation entropy due to orientational reorganization of the solvent and a positive solvation entropy due to density reorganization. The Onsager model does not provide even a qualitative account of solvation entropies. Our simulations give strong support to the Q-model of nonlinear solvation. Applications of the dipole solvation thermodynamics to electron-transfer reactions and optical spectroscopy are discussed.