This paper describes a probabilistic method for real-time decision making and motion planning for autonomous vehicles. Our approach relies on that driving on road networks implies a priori defined requirements that the motion planner should satisfy. Starting from an initial state of the vehicle, a map, the obstacles in the region of interest, and a goal region, we formulate the motion-planning problem as a nonlinear nonGaussian estimation problem, which we solve using particle filtering. We assign probabilities to the generated trajectories according to their likelihood of obeying the driving requirements. Decision making and collision avoidance is naturally integrated in the approach. We develop a receding-horizon implementation and verify the method in simulated real road scenarios and in an experimental validation using a scaled mobile robot setup with car-like dynamics. The results show that the method generates dynamically feasible trajectories for a number of scenarios, such as collision avoidance, overtaking, and traffic-jam scenarios. In addition, the computation times and memory requirements indicate that the method is suitable for real-time implementation.