In this paper, we investigate antenna selection strategies for MIMO-OFDM wireless systems from an energy efficiency perspective. We first derive closed-form expressions of the energy efficiency and the energy efficiency- spectral efficiency (EE-SE) trade-off in conventional antenna selection MIMO-OFDM systems. The obtained results show that these systems suffer from a significant loss in energy efficiency. To achieve a better energy-efficiency performance, we propose an adaptive antenna selection method where both the number of active RF (radio frequency) chains and the antenna indices are selected depending on the channel condition. This selection scheme could be implemented by an exhaustive search technique for a small number of antennas. Moreover, we develop a greedy algorithm that achieves a near-optimal performance with much lower complexity compared to the (optimal) exhaustive search method when the number of antennas is large. In addition, the efficacy of power loading across subcarriers for improved energy efficiency in the conventional and proposed antenna selection MIMO-OFDM systems is considered. Monte-Carlo simulation results are provided to validate our analyses.