Based on an extensive set of density functional theory calculations it is shown that for a class of catalytic reactions there is a universal, reactant independent relation between the reaction activation energy and the stability of reaction intermediates. This leads directly to a universal relationship between adsorption energies and catalytic activity, which is used to pinpoint what it is that determines the best catalyst for a given reaction. The universality principle rationalizes a number of known facts about catalysts and points to new ways of improving them.