Low-temperature scanning tunneling spectroscopy of magnetic and non-magnetic metal atoms on Ag(111) and on Cu(111) surfaces reveals the existence of a common electronic resonance at an energy below the binding energies of the surface states. Using an extended Newns-Anderson model, we assign this resonance to an adsorbate-induced bound state, split off from the bottom of the surface-state band, and broadened by the interaction with bulk states. A lineshape analysis of the bound state indicates that native adatoms decrease the surface-state lifetime, while a cobalt adatom causes no significant change.