The adsorption and activation of CO over flat Co {0001}, corrugated Co {1120}, and stepped Co {1012} and Co {1124} surfaces have been analyzed using periodic density functional theory calculations. CO strongly chemisorbs on all these surfaces but does not show a strong dependence on the surface structure. The calculated structure of adsorbed CO on Co {0001} at 1/3 monolayer (ML) of coverage was found to be in good agreement with the experiment. The barrier for CO dissociation over Co {0001} was found to decrease with decreasing CO coverage, taking on a value of 232 kJ/mol at 1/4 ML and 218 kJ/mol at 1/9 ML. The presence of the "zigzag" channel on Co {1120} enhances the reactivity slightly by reducing the barrier for CO dissociation to 195 kJ/mol. In contrast, the stepped Co {1012} and Co {1124} surfaces are much more active than the flat and corrugated surfaces. Both stepped surfaces provide direct channels for CO dissociation that do not have barriers with respect to gas-phase CO. In general the activation barriers lower as the reaction energies become more exothermic. Reconstruction of the step edges that occur in the product state, however, prevents a linear correlation between the reaction energy and the activation energy.