Estimating the intentions and trajectories of other vehicles is critical to achieving stable, long-term planning and decision making in autonomous driving systems. This paper introduces a novel technique for estimating the intention and trajectory probabilities of surrounding vehicles. The first step is to use a deterministic behavior planner to identify possible trajectories and behaviors. The behavior planner models an average driver who follows the driving rules according to information provided by a road network map, and also provides the control signal used in the following step. Next, a customized particle filter is integrated with the planner to model the uncertainty of various trajectories and behaviors, using multiple sensing cues such as pose, velocity, acceleration and turn signal use. The proposed method supports various sensor modalities, depending on the availability of additional sensing information. Finally, by including the sensor data the probabilistic process is able to estimate the probabilities of various trajectories and intentions. The proposed method is generic to any driving situation supported by the behavior planner. Intentions such as 'go forward', 'turn right', 'turn left', 'yield' and 'stop' are supported by the proposed method. Our proposed method is evaluated using multiple, complex, simulated driving situations, and then comparing the simulation's ground truth to the estimated probabilities. Evaluation criteria are how early and accurately our system can estimate the driving trajectory and intention probabilities of the vehicle. Our results show that the method can successfully estimate driver intention and trajectory in multiple complex situations, such as left turns, right turns and during passing, as well as at four-way intersections and bus stops.