Conventional density-functional theory (DFT) has the potential to overbind radical molecule complexes because of erroneous charge transfer. We examined this behavior by exploring the ability of various DFT approximations to predict fractional charge transfer and by quantifying the overbinding in a series of complexes. It is demonstrated that too much charge is transferred from molecules to radicals when the radical singly unoccupied molecular orbitals are predicted to be erroneously too low in energy relative to the molecule highest occupied molecular orbitals, leading to excessive Coulombic attraction. In this respect, DFT methods formulated with little or no Hartree-Fock exchange perform most poorly. The present results illustrate that the charge-transfer problem is much broader than may have been previously expected and is not limited to conventional (i.e., molecule-molecule) donor-acceptor complexes.