The success of density functional theory for the description of the adsorption of atoms on surfaces is well established and, based on recent calculations using gradient corrections, it has been shown that it also describes well the dissociative adsorption of molecules at surfaces — admittedly, however, the database for reactions at surfaces is still somewhat small. In this paper the power of density functional theory calculations is demonstrated through investigations for two different adsorption systems, namely one with a strongly electropositive adsorbate [Na on Al(111)] and one with a strongly electronegative adsorbate [O on Ru(0001)]. In each case, new hitherto unexpected adsorbate phases have been predicted by the theory: for Na on Al(111) the stability of a “four-layer” surface alloy was identified while for O on Ru(0001) it was predicted that the formation of a (1×1)-O adlayer should be possible which implies that the apparent saturation coverage of Θo=1/2 is due to kinetic hindering.