I examine localized kinetic terms for gauge fields which can propagate into compact extra dimensions. I find that such terms are generated by radiative corrections in both theories with matter fields confined to branes and in theories imposing orbifold boundary conditions on bulk matter. In both cases, the radiative corrections are logarithmically divergent, indicating that from an effective field theory point of view they cannot be predicted in terms of other parameters, and should be treated as independent leading order parameters of the theory. Specializing to the five dimensional case, we show that these terms may result in gross distortions of the Kaluza-Klein gauge field masses, wave functions, and couplings to brane and bulk matter. The resulting phenomenological implications both in flat extra dimensions, and in the warped scenario, are discussed.