Micro-Doppler signatures can be used not only to recognize different targets, such as vehicles, helicopters, animals, and people, but also to classify varying activities, e.g., walking, running, creeping, and crawling. For this purpose, a plethora of features have been proposed in the literature; however, dozens of features are not required to achieve high classification performance. The topic of feature selection has been under addressed in micro-Doppler studies. Moreover, the optimal feature set is not static but varies under different operational conditions, such as signal-to-noise ratio (SNR), dwell time, and aspect angle. The mutual information of features relative to the classification problem at hand offers a measure for assessing the efficacy of features and thus sets a unique framework for feature selection. In this paper, information-theoretic (IT) feature selection techniques are used to identify essential features and minimize the total number of required features, while maximizing classification performance. It is seen that, although some features are consistently preferred, others are never selected. Results show that for SNRs over 10 dB and at least 1 s of data, this approach yields 96% correct classification when the target moves along the radar line-of-sight and over 65% correct classification for tangential motion.