Ranking systems are a fundamental ingredient of multi-agent environments and Internet Technologies. These settings can be viewed as social choice settings with two distinguished properties: the set of agents and the set of alternatives coincide, and the agents' preferences are dichotomous, and therefore classical impossibility results do not apply. In this paper we initiate the study of incentives in ranking systems, where agents act in order to maximize their position in the ranking, rather than to obtain a correct outcome. We consider several basic properties of ranking systems, and fully characterize the conditions under which incentive compatible ranking systems exist, demonstrating that in general no such system satisfying all the properties exists.