File sharing over peer-to-peer networks has been one of the most important Internet applications over the past fifteen years, with a vast number of users and nodes participating to these networks every day. Given the large sets of computing resources involved in peer-to-peer file sharing networks, their aggregate energy consumption is an important problem to be addressed, considered the economic and environmental impact of energy production and use. In this paper we evaluate how the sleep-and-wake energy-saving approach can be used to reduce energy consumption in Gnutella, one of the most popular peer-to-peer file sharing networks. In order to save energy, we introduce a general sleep-and-wake algorithm that allows leaf-peers of the Gnutella network cyclically switch between wake and sleep mode, where the time passed in sleep mode is autonomously decided by each leaf-peer. We define different strategies that a leaf-peer may employ to decide the duration of its sleep periods. Such strategies are evaluated through simulation using the general sleep-and-wake algorithm in different network scenarios.