We predict entity type distributions in Web search queries via probabilistic inference in graphical models that capture how entitybearing queries are generated. We jointly model the interplay between latent user intents that govern queries and unobserved entity types, leveraging observed signals from query formulations and document clicks. We apply the models to resolve entity types in new queries and to assign prior type distributions over an existing knowledge base. Our models are efficiently trained using maximum likelihood estimation over millions of real-world Web search queries. We show that modeling user intent significantly improves entity type resolution for head queries over the state of the art, on several metrics, without degradation in tail query performance.