Stimulated by the increasing interest in ion adsorption effects on electrocatalytic reactions and by recent more detailed reports on the potential dependent adlayer structures formed on Ru(0001) in pure HClO4 and H2SO4 electrolytes, we revisited the oxygen reduction reaction (ORR) on structurally well-defined Ru(0001) single crystal surfaces prepared under ultrahigh vacuum conditions. We demonstrate that the complex, potential-dependent activity both for the ORR and for H2O2 formation is closely related to potential-dependent changes in the composition and structure of the adlayer. Our results demonstrate the enormous effects adsorbed species can have on the ORR reaction characteristics, either by surface blocking, e.g., by (co-)adsorbed bisulfate species, or by participation in the reaction, e.g., by *H transfer from adsorbed H or OH to O2. The comparison with results obtained on polycrystalline Ru, which differ significantly from Ru(0001) data, furthermore underlines the importance of using structurally well-defined surfaces as a reference system for future theoretical studies.