In this paper, we present a systematic angle-resolved photoemission (ARUPS) study on prototypical adsorbate systems consisting of a rare-gas monolayer (At, Kr, Xe) on a noble-metal (111) surface(Cu, Ag, Au). Although the coupling between substrate and physisorbed overlayer is weak, there is a significant influence on the Shockley-type surface state that is still observable on the well-ordered monolayer systems. The results show that there is an immediate correspondence between the surface-state binding energy and the nobleness of the rare-gas adsorbates, reflecting the short-range repulsive forces between adsorbate and substrate. In the case of Au(111), one can observe an increase of the spin-orbit splitting of the Shockley state with decreasing nobleness. In addition, we discuss the influence of the root3 x root3R30degrees Xe superlattice on the surface electronic structure of Cu(111).