A systematic investigation has been carried out of the accuracy of molecular equilibrium structures of 19 small closed-shell molecules containing first-row atoms as predicted by the following standard electronic nb initio models : Hartree-Fock (HF) theory, Moller-Plesset theory to second, third, and fourth orders (MP2, MP3, and MP4), coupled-cluster singles and doubles (CCSD) theory; CCSD theory with perturbational triples corrections [CCSD(T)], and the configuration-interaction singles and doubles (CISD) model. For all models, calculations were carried out using the correlation-consistent polarized valence double-zeta (cc-pVDZ) basis, the correlation-consistent polarized valence triple-zeta (cc-pVTZ) basis, and the correlation-consistent polarized valence quadruple-zeta (cc-pVQZ) basis. Improvements in the basis sets shorten the bond distances at all levels. Going from cc-pVDZ to cc-pVTZ, bond distances are on the average reduced by 0.8 pm at the Hartree-Fock level and by 1.6 pm at the correlated levels. From cc-pVTZ to cc-pVQZ, the contractions are about ten times smaller and the cc-pVTZ basis set appears to yield bond distances close to the basis-set limit for all models. The models HF, MP2, and CCSD(T) give improved accuracy at increased computational cost. The accuracy of the Moller-Plesset series oscillates, with MP3 being considerably less accurate than MP2 and MP4. The MP2 geometries are remarkably accurate, being only very slightly improved upon at the MP4 level for the cc-pVQZ basis. The CCSD equilibrium structures are only moderately accurate, being intermediate between MP2 and MP3. The accuracy of the CCSD(T) model, in contrast, is high and comparable to that observed in most experimental studies and it has been used to challenge the experimentally determined equilibrium structure of HNO. The CISD wave function provides structures of low quality.