We introduce a new entity typing task: given a sentence with an entity mention, the goal is to predict a set of free-form phrases (e.g. skyscraper, songwriter, or criminal) that describe appropriate types for the target entity. This formulation allows us to use a new type of distant supervision at large scale: head words, which indicate the type of the noun phrases they appear in. We show that these ultra-fine types can be crowd-sourced, and introduce new evaluation sets that are much more diverse and fine-grained than existing benchmarks. We present a model that can predict ultra-fine types, and is trained using a multitask objective that pools our new head-word supervision with prior supervision from entity linking. Experimental results demonstrate that our model is effective in predicting entity types at varying granularity; it achieves state of the art performance on an existing fine-grained entity typing benchmark, and sets baselines for our newly-introduced datasets.