Understanding the intentions of drivers at intersections is a critical component for autonomous vehicles. Urban intersections that do not have traffic signals are a common epicentre of highly variable vehicle movement and interactions. We present a method for predicting driver intent at urban intersections through multi-modal trajectory prediction with uncertainty. Our method is based on recurrent neural networks combined with a mixture density network output layer. To consolidate the multi-modal nature of the output probability distribution, we introduce a clustering algorithm that extracts the set of possible paths that exist in the prediction output, and ranks them according to likelihood. To verify the method's performance and generalizability, we present a real-world dataset that consists of over 23,000 vehicles traversing five different intersections, collected using a vehicle mounted Lidar based tracking system. An array of metrics is used to demonstrate the performance of the model against several baselines.