Many fields view stochasticity as a way to gain computational efficiency, while often having to trade off accuracy. In this perspective article, we argue that stochasticity plays a fundamentally different role in machine learning (ML) and is likely a critical ingredient of intelligent systems. As we review the ML literature, we notice that stochasticity features in many ML methods, affording them robustness, generalizability, and calibration. We also note that randomness seems to be prominent in biological intelligence, from the spiking patterns of individual neurons to the complex behavior of animals. We conclude with a discussion of how we believe stochasticity might shape the future of ML.