The aromaticity and antiaromaticity of the ground state (S-0), lowest triplet state (T-1), and first singlet excited state (S-1) of benzene, and the ground states (SO), lowest triplet states (T-1), and the first and second singlet excited states (S-1 and S-2) of square and rectangular cyclobutadiene are assessed using various magnetic criteria including nucleus-independent chemical shifts (NICS), proton shieldings, and magnetic susceptibilities calculated using complete-active-space self-consistent field (CASSCF) wave functions constructed from gauge-including atomic orbitals (GIAOs). These magnetic criteria strongly suggest that, in contrast to the well-known aromaticity of the So state of benzene, the T, and S, states of this molecule are antiaromatic. In square cyclobutadiene, which is shown to be considerably more antiaromatic than rectangular cyclobutadiene, the magnetic properties of the T, and S, states allow these to be classified as aromatic. According to the computed magnetic criteria, the T] state of rectangular cyclobutadiene is still aromatic, but the S, state is antiaromatic, just as the S2 state of square cyclobutadiene; the S2 state of rectangular cyclobutadiene is non-aromatic. The results demonstrate that the well-known "triplet aromaticity" of cyclic conjugated hydrocarbons represents a particular case of a broader concept of excited-state aromaticity and anti aromaticity. It is shown that while electronic excitation may lead to increased nuclear shieldings in certain low-lying electronic states, in general its main effect can be expected to be nuclear deshielding, which can be substantial for heavier nuclei.