The Hartree-Fock and correlation contributions to the interaction energy of the hydrogen-bonded complexes (HF)(2), (HCl)(2), H2OHF, HCNHF, and (H2O)(2) are computed in conventional calculations employing the aug-cc-pVXZ series of basis sets at the levels of Hartree-Fock theory, second-order perturbation theory, and coupled-cluster theory with single and double excitations augmented by a perturbative triples correction. The basis set convergence of the interaction energy is examined by comparison with results obtained with an explicitly correlated wave function model. The counterpoise-corrected and uncorrected Hartree-Fock interaction energies both converge very unsystematically. The convergence of the uncorrected correlation contribution is also very unsystematic because the basis set superposition error and the error from the incomplete description of the electronic Coulomb cusp both are present. Once the former has been effectively removed by the counterpoise correction, the cusp dominates and the convergence of the counterpoise-corrected correlation contribution follows an X-3 form similar to the form for the correlation energy. Two-point extrapolated values obtained with this form are close to the basis set limit and represent a significant improvement on the unextrapolated results.