Online offerings such as web search, news portals, and e-commerce applications face the challenge of providing high-quality service to a large, heterogeneous user base. Recent efforts have highlighted the potential to improve performance by introducing methods to personalize services based on special knowledge about users and their context. For example, a users demographics, location, and past search and browsing may be useful in enhancing the results offered in response to web search queries. However, reasonable concerns about privacy by both users, providers, and government agencies acting on behalf of citizens, may limit access by services to such information. We introduce and explore an economics of privacy in personalization, where people can opt to share personal information, in a standing or on-demand manner, in return for expected enhancements in the quality of an online service. We focus on the example of web search and formulate realistic objective functions for search efficacy and privacy. We demonstrate how we can find a provably near-optimal optimization of the utility-privacy tradeoff in an efficient manner. We evaluate our methodology on data drawn from a log of the search activity of volunteer participants. We separately assess users' preferences about privacy and utility via a large-scale survey, aimed at eliciting preferences about peoples' willingness to trade the sharing of personal data in returns for gains in search efficiency. We show that a significant level of personalization can be achieved using a relatively small amount of information about users.