Negative cooperativity is a phenomenon in which the binding of one or more molecules of a ligand to a multimeric receptor makes it more difficult for subsequent ligand molecules to bind. Negative cooperativity can make a multimeric receptor's response more graded than it would otherwise be. However, through theory and experimental results, we show that if the ligand binds the receptor with high affinity and can be appreciably depleted by receptor binding, then negative cooperativity produces a qualitatively different type of response: a highly ultrasensitive response with a pronounced threshold. Because ultrasensitivity and thresholds are important for generating various complex systems-level behaviors, including bistability and oscillations, negative cooperativity may be an important ingredient in many types of biological responses.