Many commercial websites use recommender systems to help customers locate products and content. Modern recommenders are based on collaborative filtering: they use patterns learned from users' behavior to make recommendations, usually in the form of related-items lists. The scale and complexity of these systems, along with the fact that their outputs reveal only relationships between items (as opposed to information about users), may suggest that they pose no meaningful privacy risk. In this paper, we develop algorithms which take a moderate amount of auxiliary information about a customer and infer this customer's transactions from temporal changes in the public outputs of a recommender system. Our inference attacks are passive and can be carried out by any Internet user. We evaluate their feasibility using public data from popular websites Hunch, Last.fm, LibraryThing, and Amazon.