This paper addresses a growing need for automation in surveillance. The aim is to ameliorate the burden on humans in conventional surveillance systems by incorporating intelligent interfaces, computer vision, and autonomous mobile robots. Besides pushing the envelope of surveillance technology, our system provides a novel context for applying planning research, which is the focus of this paper. We frame the robot surveillance planning problem, describing how the integration of components in our system supports fully-automated decision-making. Several concrete scenarios deployed in real surveillance environments exemplify both the flexibility of our system to experiment with different representations and algorithms \emph{and} the portability of our system into a variety of problem contexts. Moreover, these scenarios demonstrate how planning enables robots to effectively balance surveillance objectives, autonomously performing the jobs of human patrols and responders.