With power a major limiting factor in the design of scalable interconnected systems, power-aware networks will become inherent components of single-chip and multi-chip systems. As communication links consume significant power regardless of utilization, we propose and investigate power-aware networks whose links are turned on and off in response to bursts and dips in traffic. We explore the design space of such on/off networks, outlining a 5-step design methodology along with solutions at each step that can form the building blocks of numerous designs. Two specific designs targeting links with substantially different on/off times are then presented and evaluated. Our simulations show that up to 54.4% power savings can be achieved along with at most 7.5% increase in latency.