The dynamics of peer participation, or churn, are an inherent property of Peer-to-Peer (P2P) systems and critical for design and evaluation. Accurately characterizing churn requires precise and unbiased information about the arrival and departure of peers, which is challenging to acquire. Prior studies show that peer participation is highly dynamic but with conflicting characteristics. Therefore, churn remains poorly understood, despite its significance. In this paper, we identify several common pitfalls that lead to measurement error. We carefully address these difficulties and present a detailed study using three widelydeployed P2P systems: an unstructured file-sharing system (Gnutella), a content-distribution system (BitTorrent), and a Distributed Hash Table (Kad). Our analysis reveals several properties of churn: (i) overall dynamics are surprisingly similar across different systems, (ii) session lengths are not exponential, (iii) a large portion of active peers are highly st...