Solvation free energies can now be calculated precisely from molecular simulations, providing a valuable test of the energy functions underlying these simulations. Here we briefly review alchemical approaches for calculating the solvation free energies of small, neutral organic molecules from molecular simulations and illustrate these approaches by applying them to calculate aqueous solvation free energies (hydration free energies). These approaches use a nonphysical pathway to compute free energy differences from a simulation or set of simulations and appear to be a particularly robust and general-purpose approach for this task. We also present an update (version 0.5) to our FreeSolv database of experimental and calculated hydration free energies of neutral compounds and provide input files in formats for several simulation packages. This revision to FreeSolv provides calculated values generated with a single protocol and software version rather than the heterogeneous protocols used in the prior version of the database. We also further update the database to provide calculated enthalpies and entropies of hydration and some experimental enthalpies and entropies as well as electrostatic and nonpolar components of solvation free energies.