Time-dependent density functional theory (TDDFT) is applied to calculate vertical excitation energies of trans-1,3-butadiene, trans-trans-1,3,5-hexatriene, all-trans-1,3,5,7-octatetraene, and all-trans-1,3,5,7,9-decapentaene. Attachment and detachment densities for transitions in butadiene and decapentaene from the ground state to the 2 (1)A(g) and 1 B-1(u) excited states are also calculated and analyzed. Based on comparisons with experimental results and high level ab initio calculations in the literature, significant improvement over configuration-interaction singles is observed for the 2 (1)A(g) state of the polyenes, which has been known to have significant double excitation character. For the 1 B-1(u) state, TDDFT underestimates the excitation energy by 0.4-0.7 eV. In this case we have observed a significant difference between the results for TDDFT and TDDFT within the Tamm-Dancoff approximation, both in excitation energies and, at least for butadiene, in the character of the excited state.