The predictive information, the mutual information between the past and future, has been shown to be a useful representation learning auxiliary loss for training reinforcement learning agents, as the ability to model what will happen next is critical to success on many control tasks. While existing studies are largely restricted to training specialist agents on single-task settings in simulation, in this work, we study modeling the predictive information for robotic agents and its importance for general-purpose agents that are trained to master a large repertoire of diverse skills from large amounts of data. Specifically, we introduce Predictive Information QT-Opt (PI-QT-Opt), a QT-Opt agent augmented with an auxiliary loss that learns representations of the predictive information to solve up to 297 vision-based robot manipulation tasks in simulation and the real world with a single set of parameters. We demonstrate that modeling the predictive information significantly improves success rates on the training tasks and leads to better zero-shot transfer to unseen novel tasks. Finally, we evaluate PI-QT-Opt on real robots, achieving substantial and consistent improvement over QT-Opt in multiple experimental settings of varying environments, skills, and multi-task configurations.