Hybrid analog-digital transceivers are employed with the view to reduce the hardware complexity and the energy consumption in millimeter wave/large antenna array systems by reducing the number of their radio frequency (RF) chains. However, the analog processing network requires power for its operation and it further introduces power losses, dependent on the number of the transceiver antennas and RF chains that have to be compensated. Thus, the reduction in the power consumption is usually much less than it is expected and given that the hybrid solutions present in general inferior spectral efficiency than a fully digital one, it is possible for the former to be less energy efficient than the latter in several cases. Existing approaches propose hybrid solutions that maximize the spectral efficiency of the system without providing any insight on their energy requirements/efficiency. To that end, in this paper, a novel algorithmic framework is developed based on which energy efficient hybrid transceiver designs are derived and their performance is examined with respect to the number of RF chains and antennas. Solutions are proposed for fully and partially connected hybrid architectures and for both single-and multi-carrier systems under the orthogonal frequency division multiplexing modulation. Simulations and theoretical results provide insight on the cases, where a hybrid transceiver is the most energy efficient solution or not.