A comparison of results obtained by three widely used DFT formalisms (BLYP, B3LYP, and BH&HLYP) with those of MO methods (MP2 and CCSD(T)) points out that the DFT approaches under consideration fail to predict the behavior of the hydrogen atom in its addition and elimination reactions, either in radicals and radical cations or in triplet states. While in some cases DFT cannot recover the existence of low-lying transition structures, in other cases the relevant transition structures could be located using DFT, but the associated barrier heights are too low relative to MO values, and serious geometrical deviations occur. Calculations using the 6-31G(d,p) and 6-311++G(d,p) basis sets show that the basis exerts a significant effect on DFT results. It can be seen that the hybrid DFT schemes which include some exact HF exchange (BH&HLYP and B3LYP) yield an improvement over the pure DFT BLYP functional (with respect to the MO values), although serious discrepancies still exist.