The reliability of density functional theory (DFT) for the prediction of equilibrium molecular properties is assessed for several challenging molecules (F-2(+), O-2(+), O-2, O-4(+), F-4(+), and NO3) which tend to artifactually break spatial symmetry in the Hartree-Fock approximation. DFT appears to be among the more robust methods for such cases, but it is not immune to anomalous property predictions. The BLYP and BPW91 functionals fail dramatically for rectangular O-4(+) and F-4(+), where they are unable to find a bound minimum.