Autonomous driving presents one of the largest problems that the robotics and artificial intelligence communities are facing at the moment, both in terms of difficulty and potential societal impact. Self-driving vehicles (SDVs) are expected to prevent road accidents and save millions of lives while improving the livelihood and life quality of many more. However, despite large interest and a number of industry players working in the autonomous domain, there still remains more to be done in order to develop a system capable of operating at a level comparable to best human drivers. One reason for this is high uncertainty of traffic behavior and large number of situations that an SDV may encounter on the roads, making it very difficult to create a fully generalizable system. To ensure safe and efficient operations, an autonomous vehicle is required to account for this uncertainty and to anticipate a multitude of possible behaviors of traffic actors in its surrounding. We address this critical problem and present a method to predict multiple possible trajectories of actors while also estimating their probabilities. The method encodes each actor's surrounding context into a raster image, used as input by deep convolutional networks to automatically derive relevant features for the task. Following extensive offline evaluation and comparison to state-of-the-art baselines, the method was successfully tested on SDVs in closed-course tests.