Despite the importance and pervasiveness of Wikipedia as one of the largest platforms for open knowledge, surprisingly little is known about how people navigate its content when seeking information. To bridge this gap, we present the first systematic large-scale analysis of how readers browse Wikipedia. Using billions of page requests from Wikipedia's server logs, we measure how readers reach articles, how they transition between articles, and how these patterns combine into more complex navigation paths. We find that navigation behavior is characterized by highly diverse structures. Although most navigation paths are shallow, comprising a single pageload, there is much variety, and the depth and shape of paths vary systematically with topic, device type, and time of day. We show that Wikipedia navigation paths commonly mesh with external pages as part of a larger online ecosystem, and we describe how naturally occurring navigation paths are distinct from targeted navigation in lab-based settings. Our results further suggest that navigation is abandoned when readers reach low-quality pages. Taken together, these insights contribute to a more systematic understanding of readers' information needs and allow for improving their experience on Wikipedia and the Web in general.