The properties of the neutrino charge radius (NCR) and anapole moments (AM's) of elementary fermions, nucleons, and nuclei are discussed. The dependence of these off-shell electromagnetic couplings on the weak gauge parameter is explicitly demonstrated by a calculation performed in the Rξ gauge. The gauge dependence of the AM's and NCR implies that they cannot be observed in isolation from other second-order, electroweak effects. It is shown, however, that the AM's of various hadronic systems having an SU(2)L quantum number TL3=0 can be considered ``observables'' in certain formal, though unphysical, limits. It is argued that, apart from these special limits, the AM is a physically meaningful entity only for heavy and/or nearly degenerate nuclei.