We analyze the impact of cooperation on the energy efficiency of two-hop relay transmissions. While cooperation has been demonstrated to improve spectral efficiency, the benefits in terms of energy consumption are not well characterized. We show that cooperation is not always beneficial in this context, since the energy required to facilitate the cooperation can sometimes outweigh its benefit. In this work, we first characterize the optimal energy efficient strategy for a single source-destination transmission aided by multiple relay nodes as a function of network parameters and the transmission rate. We then extend this result to a relay-assisted cellular broadcast network and determine optimal solution which provides guidelines on the cooperative strategy that improves energy efficiency in such networks.