We describe atomistic simulations of the free energy and entropy of hydration of ions in aqueous solution at 25 degrees C using a simple point charge model (SPC/E) for water and charged spherical Lennard-Jones solutes, We use a novel method with an extended Lagrangian or Hamiltonian in which the charge and the size of the ions are considered as dynamical variables. This enables us to determine thermodynamic properties as continuous functions of solute size and charge and to move smoothly from hydrophilic to hydrophobic solvation conditions. On passing between these extremes, the entropy of solvation goes through maxima. For example it shows a double maximum as a function of charge at constant size and a single maximum as a function of size at constant (non-zero) charge, These maxima correspond to extremes of structure-breaking and are associated with the disappearance of the second solvation shell in the radial distribution function; no anomalies are seen in the first shell. We also present direct evidence of the asymmetry in the free energy, enthalpy and entropy of hydration of ions on charge inversion arising from the asymmetry in the charge distribution in a water molecule. Our calculation only includes local contributions to the thermodynamic functions, but once finite size corrections are applied, the results are in reasonable agreement with experiment.