Wikipedia is one of the most popular sites on the Web, with millions of users relying on it to satisfy a broad range of information needs every day. Although it is crucial to understand what exactly these needs are in order to be able to meet them, little is currently known about why users visit Wikipedia. The goal of this paper is to fill this gap by combining a survey of Wikipedia readers with a log-based analysis of user activity. Based on an initial series of user surveys, we build a taxonomy of Wikipedia use cases along several dimensions, capturing users' motivations to visit Wikipedia, the depth of knowledge they are seeking, and their knowledge of the topic of interest prior to visiting Wikipedia. Then, we quantify the prevalence of these use cases via a large-scale user survey conducted on live Wikipedia with almost 30,000 responses. Our analyses highlight the variety of factors driving users to Wikipedia, such as current events, media coverage of a topic, personal curiosity, work or school assignments, or boredom. Finally, we match survey responses to the respondents' digital traces in Wikipedia's server logs, enabling the discovery of behavioral patterns associated with specific use cases. For instance, we observe long and fast-paced page sequences across topics for users who are bored or exploring randomly, whereas those using Wikipedia for work or school spend more time on individual articles focused on topics such as science. Our findings advance our understanding of reader motivations and behavior on Wikipedia and can have implications for developers aiming to improve Wikipedia's user experience, editors striving to cater to their readers' needs, third-party services (such as search engines) providing access to Wikipedia content, and researchers aiming to build tools such as recommendation engines.