Density-functional theory (DFT) is widely used for studying large systems such as metals, semiconductors, and large molecules, with time-dependent density-functional theory becoming a very powerful tool for investigating molecular excited states. As part of a systematic study of both the intrinsic weaknesses of DFT and the weaknesses of present implementations, we consider its application to the one and two-dimensional conjugated pi systems: polyacetylene fragments and oligoporphyrins, respectively. Very poor results are obtained for the calculated spectra, and polyacetylene is predicted by all functionals considered, including gradient-corrected functionals, to have a triplet ground state. The cause of this is linked to known problems of existing density functionals concerning nonlocality and asymptotic behavior which result in the highest-occupied molecular-orbital being too high in energy so that semiconductors and low-band-gap insulators are predicted to have metal-like properties. The failure of modern density functionals to predict qualitatively realistic molecular hyperpolarizabilities for extended systems is closely related.