The access network is believed to account for 70-80% of the overall energy consumption of wired networks, attributable in part to the large number of small and inefficient switches deployed in typical homes and enterprises. In order to reduce the per-bit energy consumption of such devices, the Energy Efficient Ethernet (EEE) standard was approved as IEEE 802.3az in 2010 with the aim of making Ethernet devices more energy efficient. However, the potential for energy savings, and their dependence on traffic characteristics, is poorly understood. This paper undertakes a comprehensive study of the energy efficiency of EEE, and makes three new contributions: First, we perform extensive measurements on three commercial EEE switches, and show how their power consumption profile depends on factors such as port counts, traffic loads, packet sizes, and traffic burstiness. Second, we develop a simple yet powerful model that gives analytical estimates of the power consumption of EEE switches under various traffic conditions. Third, we validate the energy savings via experiments in typical deployment scenarios, and estimate the overall reduction in annual energy costs that can be realized with widespread adoption of EEE in the Internet.