In this paper, time-dependent density functional theory (TDDFT) calculations of excited state polarizabilities of conjugated molecules are presented. The increase in polarizability upon excitation was obtained by evaluating the dependence of the excitation energy on an applied static electric field. The excitation energy was found to vary quadratically with the field strength. The excess polarizabilities obtained for singlet excited states are in reasonable agreement with the experimental results for the shorter oligomers, particularly if the experimental uncertainties are considered. For longer oligomers the excess polarizability is considerably overestimated, similar to DFT calculations of ground state polarizabilities. Excess polarizabilities of triplet states were found to be smaller than those for the corresponding singlet state, which agrees with experimental results that are available for triplet polarizabilities. Negative polarizabilities are obtained for the lowest singlet A(g) states of longer oligomers. The polarizability of the lowest B-u and A(g) excited states of the conjugated molecules studied here are determined mainly by the interaction between these two states. Upon application of a static electric field a quadratic Stark effect is observed in which the lower B-u state has a positive excess polarizability and the upper A(g) state exhibits a decrease in polarizability upon excitation. All results are explained in terms of a sum-over-states description for the polarizability.