We report on the spin dependence of elastic and inelastic electron tunneling through transition metal atoms. Mn, Fe and Cu atoms were deposited onto a monolayer of Cu2N on Cu(100) and individually addressed with the probe tip of a scanning tunneling microscope. Electrons tunneling between the tip and the substrate exchange energy and spin angular momentum with the surfacebound magnetic atoms. The conservation of energy during the tunneling process results in a distinct onset threshold voltage above which the tunneling electrons create spin excitations in the Mn and Fe atoms. Here we show that the additional conservation of spin angular momentum leads to different cross-sections for spin excitations depending on the relative alignment of the surface spin and the spin of the tunneling electron. For this purpose, we developed a technique for measuring the same local spin with a spin-polarized and a non-spin-polarized tip by exchanging the last apex atom of the probe tip between different transition metal atoms. We derive a quantitative model describing the observed excitation cross-sections on the basis of an exchange scattering process.