Peer-to-Peer (P2P) applications continue to grow in popularity, and have reportedly overtaken Web applications as the single largest contributor to Internet traffic. Using traces collected from a large edge network, we conduct an extensive analysis of P2P traffic, compare P2P traffic with Web traffic, and discuss the implications of increased P2P traffic. In addition to studying the aggregate P2P traffic, we also analyze and compare the two main constituents of P2P traffic in our data, namely BitTorrent and Gnutella. The results presented in the paper may be used for generating synthetic workloads, gaining insights into the functioning of P2P applications, and developing network management strategies. For example, our results suggest that new models are necessary for Internet traffic. As a first step, we present flow-level distributional models for Web and P2P traffic that may be used in network simulation and emulation experiments.