The isotropic and anisotropic hyperfine (hf) structures of a set of anionic, neutral and cationic radicals are investigated by means of local and nonlocal gradient-corrected density functional theory (DFT). The molecules under study are formed by H, C, N, O, F, and CI atoms, and the hf structures are computed at both the experimental (where present) and various DFT and CI optimized geometries. The agreement with experiment and with results from previous CI or MRCI calculations is generally very satisfactory. The anisotropic hf couplings are relatively insensitive to basis set effects and functional form, whereas the isotropic hf couplings are highly dependent on the form of the nonlocal corrections to the exchange functional, particularly for heteroatoms. Using the functional by Perdew and Wang ("PW86"), an excellent agreement with experiment is obtained for all neutral and cationic radicals, whereas for the halide containing anions somewhat elongated bond lengths, and thus less accurate hf structures, are obtained.