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This work studies the problem of predicting human intent to interact with a robot in a public environment. To facilitate research in this problem domain, we first contribute the People Approaching Robots Database (PAR-D), a new collection of datasets for intent prediction in Human-Robot Interaction. The database includes a subset of the ATC Approach Trajectory dataset [28] with augmented ground truth labels. It also includes two new datasets collected with a robot photographer on two locations of a university campus. Then, we contribute a novel human-annotated baseline for predicting intent. Our results suggest that the robot’s environment and the amount of time that a person is visible impacts human performance in this prediction task. We also provide computational baselines for intent prediction in PAR-D by comparing the performance of several machine learning models, including ones that directly model pedestrian interaction intent and others that predict motion trajectories as an intermediary step. From these models, we find that trajectory prediction seems useful for inferring intent to interact with a robot in a public environment.