Multi-task learning ideally allows robots to acquire a diverse repertoire of useful skills. However, many multi-task reinforcement learning efforts assume the robot can collect data from \emph{all} tasks at \emph{all} times. In reality, the tasks that the robot learns arrive sequentially, depending on the user and the robot's current environment. In this work, we study a practical sequential multi-task RL problem that is motivated by the practical constraints of physical robotic systems, and derive an approach that effectively leverages the data and policies learned for previous tasks to cumulatively grow the robot's skill-set. In a series of simulated robotic manipulation experiments, our approach requires less than half the samples than learning each task from scratch, while avoiding impractical round-robin data collection. On a Franka Emika Panda robot arm, our approach incrementally learns ten challenging tasks, including bottle capping and block insertion.