P2P systems are increasingly used for efficient, scalable data sharing. Popular applications focus on massive file sharing. However, advanced applications such as online communities (e.g., medical or research communities) need to share private or sensitive data. Currently, in P2P systems, untrusted peers can easily violate data privacy by using data for malicious purposes (e.g., fraudulence, profiling). To prevent such behavior, the well accepted Hippocratic database principle states that data owners should specify the purpose for which their data will be collected. In this paper, we apply such principles as well as reputation techniques to support purpose and trust in structured P2P systems. Hippocratic databases enforce purpose-based privacy while reputation techniques guarantee trust. We propose a P2P data privacy model which combines the Hippocratic principles and the trust notions. We also present the algorithms of PriServ, a DHT-based P2P privacy service which supports this model and prevents data privacy violation. We show, in a performance evaluation, that PriServ introduces a small overhead.