Analysis of aggregate and individual Web traffic has shown that PageRank is a poor model of how people navigate the Web. Using the empirical traffic patterns generated by a thousand users, we characterize several properties of Web traffic that cannot be reproduced by Markovian models. We examine both aggregate statistics capturing collective behavior, such as page and link traffic, and individual statistics, such as entropy and session size. No model currently explains all of these empirical observations simultaneously. We show that all of these traffic patterns can be explained by an agent-based model that takes into account several realistic browsing behaviors. First, agents maintain individual lists of bookmarks (a non-Markovian memory mechanism) that are used as teleportation targets. Second, agents can retreat along visited links, a branching mechanism that also allows us to reproduce behaviors such as the use of a back button and tabbed browsing. Finally, agents are sustained by visiting novel pages of topical interest, with adjacent pages being more topically related to each other than distant ones. This modulates the probability that an agent continues to browse or starts a new session, allowing us to recreate heterogeneous session lengths. The resulting model is capable of reproducing the collective and individual behaviors we observe in the empirical data, reconciling the narrowly focused browsing patterns of individual users with the extreme heterogeneity of aggregate traffic measurements. This result allows us to identify a few salient features that are necessary and sufficient to interpret the browsing patterns observed in our data. In addition to the descriptive and explanatory power of such a model, our results may lead the way to more sophisticated, realistic, and effective ranking and crawling algorithms.