Leonard Bernstein chose Amram in 1966 as the first composer-in-residence in New York City. Joseph Papp had earlier tapped him to score the incidental music for Shakespeare in the Park in 1957. Amram pioneered the jazz French horn, is a piano virtuoso, and is accomplished on flute, whistles, percussion and dozens of folkloric instruments and vocal improvisation.

Amram's composition of "Red River Valley Theme and Variations" is especially noteworthy, combining both the formal traditions of classical European composition and American folk music. Amram is especially well known for his collaborative tradition, having collaborated with Langston Hughes, Dizzy Gillespie, Dustin Hoffman, Thelonious Monk, Odetta, Elia Kazan, Arthur Miller, Charles Mingus, Lionel Hampton, Tito Puente, Pete Seeger and Willie Nelson.

Amram is also a favorite of children, having been featured in Raffi's hit song "Peanut Butter Sandwich, Jelly With Jam: One for Me and One for David Amram," and having made numerous appearances on "Sesame Street."

Amram has been described by the Boston Globe as the "Renaissance man of American music." He is now writing a book about his collaboration with Beat poet Jack Kerouac, with whom he performed the first jazz poetry readings in New York City in 1957. He scored and appeared with Kerouac in the 1959 Beat Generation documentary Pull My Daisy.