Prediction of solvation free energies is an important subject in fundamental natural science but also important to the pharmaceutical and food industry. A popular modeling approach is to treat the solution by an implicit solvent model. The solute molecule is rigid with a fixed effective charge distribution localized at the atomic nuclei positions. The hydration free energy is described by the van der Waals energy, the solute cavity formation energy in the water phase, and the-change in electrostatic solute-solvent interaction energy. The dielectric continuum is generally assumed to be a simple medium, that is, linear, homogeneous, and isotropic. However, this approximation is quite severe and will give too hydrophilic solvation free energies. We show here that the simple medium approximation must be relaxed and nonlinearity must be taken into consideration. In strong electric fields, the solvent polarization becomes saturated and the dielectric no longer responds linearly in the applied field. This effect is well-described by the modified Langevin-Debye model. This nonlinear solvation model is used to study the hydration of 181 small organic molecules. Atomic charges and radii of the solute molecule are described by a standard classical force field. We apply the optimized potentials for liquid simulation all atom (OPLS-AA) force field, which is parametrized to reproduce both structural and thermodynamical data. This leads to a mean unsigned error of 0.6 kcal/mol, which is a 25% improvement compared to a simple medium approach. The nonlinear solvation model is further improved by introducing a few charge-scaling parameters for some functional groups that show a systematic deviation from their experimental data. This yields a mean unsigned error of 0.4 kcal/mol, which is only twice the experimental uncertainty. Hence, we conclude that nonlinear dielectric effects are indeed important to incorporate in implicit solvent models, even for neutral polar molecules.