The energies, band orders, and spin polarizations of a series of CH2=CH-XH(n)(.) radicals were calculated at the UMP2/6-311+G(**), Becke3LYP/6-311+G(**), and QCISD/6-311G(**) theoretical levels, and the energies also were obtained at the G2(MP2) theoretical level. The energies of the parent compounds were obtained in the same fashion and their bond dissociation energies were derived from these data. The Becke3LYP and the G2(MP2) energies predicted essentially the same stabilization energies for the radicals, and stabilization was found mainly with allyl itself and with the vinyl thiol radical indicating that stabilization requires that the terminal atoms have similar electronegativities. A study of related radicals also indicated that stabilization is lost when the central atom has a different electronegativity. Therefore, stabilization of the allyl radical appears to require that all three atoms in the allyl system have similar electronegativities. It is found that the radical center prefers to be at the less electronegative atom. When the terminal atoms have similar electronegativities, the odd electron is shared between them, and the center atom becomes spin polarized in the opposite sense. Spin polarizations calculated from Becke3LYP and QCISD wave functions are essentially the same, but those calculated from MP2 wave functions are often incorrect as a result of spin contamination. The results obtained with the allyl radicals are compared with corresponding data for allyl cations and anions.