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The relative energies of the energetically low-lying tautomers of pyridone, cytosine, uracil, thymine, guanine, and iso-cytosine are studied by a variety of different quantum chemical methods. In particular, we employ density functional theory (DFT) using the six functionals HCTH407, PBE, BP86, B-LYP, B3-LYP, and BH-LYP, and the ab initio methods Hartree-Fock (HF), standard second-order Moller-Plesset perturbation theory (MP2), an improved version of it (SCS-MP2), and quadratic configuration interaction including single and double excitations (QCISD) and perturbative triple corrections [QCISD(T)]. A detailed basis set study is performed for the form amide/formamidic acid tautomeric pair. In general, large AO basis sets of at least valence triple-zeta quality including f-functions (TZV) are employed, which are found to be necessary for an accurate energetic description of the various structures. The performance of the more approximate methods is evaluated with QCISD(T)/TZV(2df,2dp) data taken as reference. In general it is found that DFT is not an appropriate method for the problem. For the tautomers of pyridone and cytosine, most density functionals, including the popular B3-LYP hybrid, predict a wrong energetic order, and only for guanine, the correct sequence of tautomers is obtained with all functionals. Out of the density functionals tested, BH-LYP, which includes a rather large fraction of HF exchange, performs best. A consistent description of the nonaromatic versus aromatic tautomers seems to be a general problem especially for pure, nonhybrid functionals. Tentatively, this could be assigned to the exchange potentials used while the functional itself, including the correlation part, seems to be appropriate. Out of the ab initio methods tested, the new SCS-MP2 approach seems to perform best because it effectively reduces some outliers obtained with standard MP2. It outperforms the much more costly QCISD method and seems to be a very good compromise between computational effort and accuracy.