By linking to external websites, Wikipedia can act as a gateway to the Web. To date, however, little is known about the amount of traffic generated by Wikipedia's external links. We fill this gap in a detailed analysis of usage logs gathered from Wikipedia users' client devices. Our analysis proceeds in three steps: First, we quantify the level of engagement with external links, finding that, in one month, English Wikipedia generated 43M clicks to external websites, in roughly even parts via links in infoboxes, cited references, and article bodies. Official links listed in infoboxes have by far the highest click-through rate (CTR), 2.47% on average. In particular, official links associated with articles about businesses, educational institutions, and websites have the highest CTR, whereas official links associated with articles about geographical content, television, and music have the lowest CTR. Second, we investigate patterns of engagement with external links, finding that Wikipedia frequently serves as a stepping stone between search engines and third-party websites, effectively fulfilling information needs that search engines do not meet. Third, we quantify the hypothetical economic value of the clicks received by external websites from English Wikipedia, by estimating that the respective website owners would need to pay a total of $7-13 million per month to obtain the same volume of traffic via sponsored search. Overall, these findings shed light on Wikipedia's role not only as an important source of information, but also as a high-traffic gateway to the broader Web ecosystem.