In wireless ad hoc networks and sensor networks, energy use is in many cases the most important constraint since it corresponds directly to operational lifetime. This paper presents two topology control protocols that extend the lifetime of dense ad hoc networks while preserving connectivity, the ability for nodes to reach each other. Our protocols conserve energy by identifying redundant nodes and turning their radios off. Geographic Adaptive Fidelity (GAF) identifies redundant nodes by their physical location and a conservative estimate of radio range. Cluster-based Energy Conservation (CEC) directly observes radio connectivity to determine redundancy and so can be more aggressive at identifying duplication and more robust to radio fading. We evaluate these protocols through analysis, extensive simulations, and experimental results in two wireless testbeds, showing that the protocols are robust to variance in node mobility, radio propagation, node deployment density, and other factors.