Provably safe motion planning for automated road vehicles must ensure that planned motions do not result in a collision with other traffic participants. This is a major challenge in autonomous driving, since the future behavior of other traffic participants is not known and since traffic participants are often hidden due to occlusions. In this work, we propose a formal setbased prediction that contains all acceptable future behaviors of both detected and potentially hidden traffic participants. Based on formalized traffic rules and nondeterministic motion models, we perform reachability analysis to predict the set of possible occupancies and velocities of vehicles, pedestrians, and cyclists. Real-world experiments with a test vehicle in various traffic situations demonstrate the applicability and real-time capability of our over-approximative prediction for both online verification and fail-safe trajectory planning. Even in congested, complex traffic scenarios, our forecasting approach enables self-driving vehicles to never cause accidents.