Measurements have been done on polarized-proton scattering from the even-mass cadmium isotopes ^106-116Cd, at a beam energy of 22.3 MeV. The experimental data were analysed using first- and second-order vibrational models in a coupled-channels formalism. The 0₁⁺, 2₁⁺ and 3₁^- levels are represented satisfactorily by theory. In ^106-116Cd the 2₂⁺ and 4₁⁺ levels were resolved; for the 2₂⁺ levels the theory systematically underestimates the first diffraction maximum of the cross section at 30 degrees while the 4₁⁺ levels are reproduced reasonably well. In ^112-114Cd the 0₂⁺ level could also be studied; there are indications for a strong coupling between the two-phonon 0⁺ state in the ground-state band and the 0⁺ head of the intruder band. In ¹¹⁴Cd we also investigated the 2₃⁺ level, probably the first excited state of the intruder system, which showed an angular pattern with more pronounced details than the 2₁⁺ states. Finally in ¹¹²Cd the 1₁^$and 5₁^- levels were studied which have a strong direct coupling to the ground state.