AI systems are increasingly pervasive, yet information needed to decide whether and how to engage with them may not exist or be accessible. A user may not be able to verify whether a system satisfies certain safety standards. An investigator may not know whom to investigate when a system causes an incident. A platform may find it difficult to penalize repeated negative interactions with the same system. Across a number of domains, IDs address analogous problems by identifying \textit{particular} entities (e.g., a particular Boeing 747) and providing information about other entities of the same class (e.g., some or all Boeing 747s). We propose a framework in which IDs are ascribed to \textbf{instances} of AI systems (e.g., a particular chat session with Claude 3), and associated information is accessible to parties seeking to interact with that system. We characterize IDs for AI systems, argue that there could be significant demand for IDs from key actors, analyze how those actors could incentivize ID adoption, explore potential implementations of our framework, and highlight limitations and risks. IDs seem most warranted in high-stakes settings, where certain actors (e.g., those that enable AI systems to make financial transactions) could experiment with incentives for ID use. Deployers of AI systems could experiment with developing ID implementations. With further study, IDs could help to manage a world where AI systems pervade society.