Most of recommender systems try to find items that are most relevant to the older choices of a given user. Here we focus on the "surprise me" query: A user may be bored with his/her usual genre of items (e.g., books, movies, hobbies), and may want a recommendation that is related, but off the beaten path, possibly leading to a new genre of books/movies/hobbies. How would we define, as well as automate, this seemingly selfcontradicting request? We introduce TANGENT, a novel recommendation algorithm to solve this problem. The main idea behind TANGENT is to envision the problem as node selection on a graph, giving high scores to nodes that are well connected to the older choices, and at the same time well connected to unrelated choices. The method is carefully designed to be (a) parameter-free (b) effective and (c) fast. We illustrate the benefits of TANGENT with experiments on both synthetic and real data sets. We show that TANGENT makes reasonable, yet surprising, horizon-broadening recommendations. Moreover, it is fast and scalable, since it can easily use existing fast algorithms on graph node proximity.