Coover was born in Charles City, Iowa. He attended Southern Illinois University Carbondale, received his B.A. in Slavic Studies from Indiana University in 1953, then served in the United States Navy. He received an M.A. in General Studies in the Humanities from the University of Chicago in 1965. In 1968, he signed the “Writers and Editors War Tax Protest” pledge, vowing to refuse tax payments in protest against the Vietnam War. Coover has served as a teacher or writer in residence at many universities. He was a professor at Brown University from 1981–2012.
Coover's wife is the noted needlepoint artist Pilar Sans Coover. They have three children, including Sara Caldwell.
Coover's first novel was The Origin of the Brunists, in which the sole survivor of a mine disaster starts a religious cult. His second book, The Universal Baseball Association, Inc., J. Henry Waugh, Prop., deals with the role of the creator. The eponymous Waugh, a shy, lonely accountant, creates a baseball game in which rolls of the dice determine every play, and dreams up players to attach those results to.
Coover's best-known work, The Public Burning, deals with the case of Julius and Ethel Rosenberg in terms that have been called magic realism. Half of the book is devoted to the mythic hero Uncle Sam of tall tales, dealing with the equally fantastic Phantom, who represents international Communism. The alternate chapters portray the efforts of Richard Nixon to find what is really going on amidst the welter of narratives.
A later novella, Whatever Happened to Gloomy Gus of the Chicago Bears offers an alternate Nixon, one who is devoted to football and sex with the same doggedness with which he pursued political success in this reality. The theme anthology A Night at the Movies includes the story "You Must Remember This", a piece about Casablanca that features an explicit description of what Rick and Ilsa did when the camera wasn't on them. Pinocchio in Venice returns to mythical themes.
Coover is one of the founders of the Electronic Literature Organization. In 1987 he was the winner of the Rea Award for the Short Story.