He was born in Kittanning, Pennsylvania, and raised in Ravenna, Ohio. Hampton was a 1960 graduate of Oberlin Conservatory and a 1963 graduate of Syracuse University. From September 1963 to June 1983 he served as organist and choirmaster of Calvary Episcopal Church in New York City in the Gramercy Park neighborhood of Manhattan. His “Fridays at Midnight” organ recital series, running from 1974 to 1983, was one of the most famous and popular organ recital series in American history.
Hampton was also a respected composer for the church and for the concert stage. Before his death, Erik Routley, a noted authority on church music, called Hampton " the greatest living composer of hymn tunes."  His settings of the Episcopal liturgy are also in use in Catholic churches, and his choral works are milestones of innovative, challenging sacred music. He also transcribed music from other sources for the organ. His versions for organ of Mussorgsky's Pictures at an Exhibition and César Franck's Symphony in D minor are noteworthy.
Hampton’s views on the proper design and function of the organ, particularly in the orchestral context, were controversial in their time because they conflicted with then-current neo-Baroque opinions.
Towards the end of his life, Hampton gave up church work and concentrated on composition and organ consulting. Several important classical instruments in the US bear the stamp of his ideas.
Weakened with AIDS, Hampton remained active until the final few weeks of his life, composing the massive Alexander Variations for two pipe organs while almost completely bedridden. He died near his parents’ home in Port Charlotte, Florida, aged 45.