This essay maintains that the question in its title is really three sets of questions: a conceptual inquiry, a moral/political inquiry, and an empirical inquiry. After devoting some attention to the relevant conceptual issues, the essay ponders in detail the moral/political issues. It suggests some answers to the germane moral/political questions, and it takes pains to distinguish those questions from other lines of inquiry with which they might be confused. Although only animals and dead people are mentioned in the title, the essay also considers whether infants, comatose people, lunatics, future generations, groups, trees, and natural phenomena such as rivers should be classified as potential holders of legal rights.