Probabilistic programming systems (PP systems) allow developers to model stochastic phenomena and perform efficient inference on the models. The number and adoption of probabilistic programming systems is growing significantly. However, there is no prior study of bugs in these systems and no methodology for systematically testing PP systems. Yet, testing PP systems is highly non-trivial, especially when they perform approximate inference. In this paper, we characterize 118 previously reported bugs in three open-source PP systems-Edward, Pyro and Stan-and propose ProbFuzz, an extensible system for testing PP systems. Prob- Fuzz allows a developer to specify templates of probabilistic models, from which it generates concrete probabilistic programs and data for testing. ProbFuzz uses language-specific translators to generate these concrete programs, which use the APIs of each PP system. ProbFuzz finds potential bugs by checking the output from running the generated programs against several oracles, including an accuracy checker. Using ProbFuzz, we found 67 previously unknown bugs in recent versions of these PP systems. Developers already accepted 51 bug fixes that we submitted to the three PP systems, and their underlying systems, PyTorch and TensorFlow.