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Task-based distributed frameworks (e.g., Ray, Dask, Hydro) have become increasingly popular for distributed applications that contain asynchronous and dynamic workloads, including asynchronous gradient descent, reinforcement learning, and model serving. As more data-intensive applications move to run on top of task-based systems, collective communication efficiency has become an important problem. Unfortunately, traditional collective communication libraries (e.g., MPI, Horovod, NCCL) are an ill fit, because they require the communication schedule to be known before runtime and they do not provide fault tolerance. We design and implement Hoplite, an efficient and fault-tolerant collective communication layer for task-based distributed systems. Our key technique is to compute data transfer schedules on the fly and execute the schedules efficiently through fine-grained pipelining. At the same time, when a task fails, the data transfer schedule adapts quickly to allow other tasks to keep making progress. We apply Hoplite to a popular task-based distributed framework, Ray. We show that Hoplite speeds up asynchronous stochastic gradient descent, reinforcement learning, and serving an ensemble of machine learning models that are difficult to execute efficiently with traditional collective communication by up to 7.8x, 3.9x, and 3.3x, respectively.