Molecular dynamics simulations in combination with the free energy perturbation technique are used in this work to calculate absolute ion hydration entropies. The hydration entropies for five alkali metal ions are estimated from van't Hoff plots using hydration free energies calculated at eight different temperatures. Considering that the ion-water potentials were parametrized only on absolute hydration free energies and ionic radii, the absolute hydration entropies agree very well with experimental data. Simulation lengths of about 3 ns at each temperature were required to achieve an uncertainty below 1 kcal/mol for the entropic contribution to the hydration free energy (-T Delta S-hyd). The uncertainties for the calculated entropies are typically four times larger than for the free energies. The possibility to use approximate approaches to calculate hydration entropies is also investigated. The entropy of creating the uncharged van der Waals spheres in water correlates well with the solvent accessible surface area of the ions. The Born continuum model and the linear response approximation cannot be used to predict the entropy of charging the van der Waals spheres in water without introducing temperature dependent empirical parameters.