We present density-functional theory and calculations for two-photon absorption spectra of molecules. The two-photon absorption cross sections are defined in terms of the single residues of the quadratic response function, which was recently derived for density-functional theory using the time-dependent variation principle and the quasi-energy ansatz. The cross-section dependence on different functionals, including the general gradient approximation and hybrid theory, is examined for a set of small molecules. The results of hybrid density-functional theory compare favorably with those from singles-and-doubles coupled-cluster response calculations.