The purpose of this dissertation is to develop a suite of privatization algorithms for symbolic systems, specifically systems modeled as Markov chains, hidden Markov models, and Markov decision processes, to protect the sensitive user data used to generate these models. We use differential privacy as our framework to provide privacy protections to user data. To enforce differential privacy for symbolic systems, we develop algorithms for privatizing reward functions, model constraints, and transition dynamics. Additionally, we develop a framework for privatizing the trajectories generated by these models, a filtering framework for these trajectories. For each framework, we provide users with tools to calibrate the strength of privacy and to analyze the accuracy of the privatized data. Future work will apply the algorithms in this dissertation to domain-specific problems, and extend these algorithms to provide privacy for continuous-time symbolic systems.