Several density functional theories, chosen among the most popular, are shown to systematically overestimate three-electron bond dissociation energies in a series of model systems covering the full range of homonuclear three-electron X∴X bonds (X = He, N, O, F, Ne, P, S, Cl, Ar) that can be found in organic cation radicals. The errors range from 15 to 54 kcal/mol with the SVWN local spin density method, from 6 to 45 kcal/mol with the gradient-corrected BLYP, BP86, and BPW91 functionals, and from 3 to 31 kcal/mol with the B3LYP, B3P86, and B3PW91 three-parameter hybrid functionals. The errors follow some regular tendencies according to the place of the X atom in the periodic table. The geometries and frequencies are also in error, the bond lengths being systematically too long and the frequencies too low. The errors are tentatively interpreted as consequences of electron self-interaction, leading to overstabilization of the Coulombic terms relative to the exchange-correlation terms in this type of bonds. At variance with these systematic errors, the BH&HLYP functional displays overall better results but still severely fails in some particular cases. Some lines of thought for devising modified DFT functionals are proposed.