Density functional calculations using both local and gradient-corrected functionals have been performed on the organic radicals CH3, CH3CH2, CH2CHCH2, CH3CHCOO-, HCOCHCOH, CH3COCHCOH, CH3COCHCOCH3, and CH3COC(CH3)COCH3. The former four radicals are used as benchmarks. The latter four radicals are derived from common organic ligands and have been observed in recent experimental work on tris(beta-ketoenolato)cobalt(III) complexes. Their geometry has been optimized both at the unrestricted Hartree-Fock level using a double-zeta basis set and at the unrestricted Kohn-Sham level using specifically optimized basis sets. From these calculations, values for the isotropic hyperfine coupling constants at the hydrogen atoms are predicted and compared with experimental data and previous results from ab initio calculations. The agreement is found to be fairly good while the computational cost remains modest, if compared with other post-Hartree-Fock methods. The dependence of the results on the geometry and on the various approximations utilized in the solution of the Kohn-Sham equations is also briefly discussed.