A systematic study of the accuracy of structures, and frequencies of 33 small radical molecules is presented as predicted by Hartree-Fock (HF) theory, second-order Moller-Plesset (MP2) theory, coupled-cluster singles and doubles (CCSD) theory, coupled-cluster singles and doubles with perturbational triples correction [CCSD(T)] theory, and gradient-corrected density functional theory with 3-parameter exact exchange mixing (B3LYP). For all methods, calculations were carried out using the Pople 6-31G**, the correlation-consistent polarized valence double-zeta (cc-pVDZ), and the correlation-consistent polarized valence triple-zeta (cc-pVTZ) basis sets. While basis set effects were moderate, large differences in the performance of the different methods were found. Due primarily to artifactual symmetry breaking and orbital instabilities, both restricted and unrestricted HF and MP2 perform too erratically to be acceptable. CCSD with either restricted or unrestricted orbitals yields results in generally good agreement with experiment. However CCSD(T) geometries and frequencies exhibit a surprising lack of improvement and in many cases are less accurate than CCSD. The accuracy of B3LYP, however, is roughly comparable, or better, to CCSD and at much reduced computational cost and therefore is a good compromise between cost and accuracy for the routine study of molecular radicals. In addition, for several radicals significant discrepancies exist between the most reliable computational methods and existing experimental data for structures and frequencies.