The performance of several direct and indirect computational strategies for the calculation of the first ionization energies (IEs) of free radicals and adiabatic detachment energies of their anions has been tested using experimental data as references. The outer valence Green's function and the partial third-order approximations, which are based on electron propagator theory, have been identified as the most accurate. They were in turn used to estimate the IEs of a large set of free radicals for which these data have not been previously reported. The calculated data also have been used to assess the possible oxidation of nucleosides by these radicals, as well as the potential, antioxidant-protection effects of phenol, catechol, ascorbic acid, and Trolox in their neutral and deprotonated forms, via electron transfer.