We propose a Deep RObust Goal-Oriented trajectory prediction Network (DROGON) for accurate vehicle trajectory prediction by considering behavioral intentions of vehicles in traffic scenes. Our main insight is that the behavior (i.e., motion) of drivers can be reasoned from their high level possible goals (i.e., intention) on the road. To succeed in such behavior reasoning, we build a conditional prediction model to forecast goal-oriented trajectories with the following stages: (i) relational inference where we encode relational interactions of vehicles using the perceptual context; (ii) intention estimation to compute the probability distributions of intentional goals based on the inferred relations; and (iii) behavior reasoning where we reason about the behaviors of vehicles as trajectories conditioned on the intentions. To this end, we extend the proposed framework to the pedestrian trajectory prediction task, showing the potential applicability toward general trajectory prediction.