Molecular dynamics/free energy perturbation simulations of several small amides [acetamide (ACT), N-methylacetamide (NMA), and N,N-dimethylacetamide] and amines [NH3, NH2CH3, NH(CH3)(2), and N(CH3)(3)] in aqueous solution were performed to study the effects on solvation free energies arising from N-methylation. Using pairwise additive potentials, a uniform pattern of solvation effects was always obtained, indicating that successive substitution of hydrogens on the nitrogen atom by hydrophobic methyl groups leads to less favorable solvation. These results are not in agreement with experimental data, which show that the solvation free energy changes associated with N-methylation are irregular and actually favor methylation in the cases of ACT --> NMA and NH3 --> NH2CH3. The amines were also studied using a many-body polarizable potential for both the solute and the solvent. The resulting salvation free energy differences represent improvements over the values obtained with the pairwise additive potentials, although the monotonic change in solvation free energy with increasing methylation persists. With the many-body polarizable potential, the magnitudes of the amine dipole moments in aqueous solution exhibit the same trend as the solvation free energies. This observation provides a basis for understanding the irregular behavior of the experimental amine solvation free energies.