The growing popularity of location-based systems, allowing unknown/untrusted servers to easily collect and process huge amounts of users' information regarding their location, has recently started raising serious concerns about the privacy of this kind of sensitive information. In this paper we study geo-indistinguishability, a formal notion of privacy for location-based systems that protects the exact location of a user, while still allowing approximate information - typically needed to obtain a certain desired service - to be released. Our privacy definition formalizes the intuitive notion of protecting the user's location within a radius r with a level of privacy that depends on r. We present three equivalent characterizations of this notion, one of which corresponds to a generalized version of the well-known concept of differential privacy. Furthermore, we present a perturbation technique for achieving geo-indistinguishability by adding controlled random noise to the user's location, drawn from a planar Laplace distribution. We demonstrate the applicability of our technique through two case studies: First, we show how to enhance applications for location-based services with privacy guarantees by implementing our technique on the client side of the application. Second, we show how to apply our technique to sanitize location-based sensible information collected by the US Census Bureau.