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Modern Reinforcement Learning (RL) algorithms promise to solve difficult motor control problems directly from raw sensory inputs. Their attraction is due in part to the fact that they can represent a general class of methods that allow to learn a solution with a reasonably set reward and minimal prior knowledge, even in situations where it is difficult or expensive for a human expert. For RL to truly make good on this promise, however, we need algorithms and learning setups that can work across a broad range of problems with minimal problem specific adjustments or engineering. In this paper, we study this idea of generality in the locomotion domain. We develop a learning framework that can learn sophisticated locomotion behavior for a wide spectrum of legged robots, such as bipeds, tripeds, quadrupeds and hexapods, including wheeled variants. Our learning framework relies on a data-efficient, off-policy multi-task RL algorithm and a small set of reward functions that are semantically identical across robots. To underline the general applicability of the method, we keep the hyper-parameter settings and reward definitions constant across experiments and rely exclusively on on-board sensing. For nine different types of robots, including a real-world quadruped robot, we demonstrate that the same algorithm can rapidly learn diverse and reusable locomotion skills without any platform specific adjustments or additional instrumentation of the learning setup.