Denver was born January 9, 1935 in New Rochelle, New York but raised in Brownwood, Texas. He graduated from Loyola University in Los Angeles, California with a degree in political science. He acted in college productions at Loyola and met fellow student Dwayne Hickman, with whom he later co-starred in The Many Loves of Dobie Gillis. After graduation, he coached physical education and taught mathematics and history at Corpus Christi School, a Roman Catholic elementary school in Pacific Palisades, California.
In 1971, Denver was arrested for possession of marijuana and drug paraphernalia in his car and pleaded no contest for a reduced sentence of a $250 fine. In 1998, he was arrested for marijuana delivered to his home, originally saying that the delivery came from Dawn Wells who played Mary Ann on Gilligan's Island, but he later refused to name her in court, testifying that "some crazy fan must have sent it." He pleaded no contest and received six months probation.
Denver died September 2, 2005 from pneumonia, at Wake Forest University Baptist Medical Center in Winston-Salem, North Carolina. He had been receiving cancer treatment and had undergone heart bypass surgery earlier that year.