- Was the first black actor to be nominated in the Best Supporting Actor category of the Academy Awards, for his role in The Reivers (1969).
- Was one of the actors Jack Nicholson dedicated his Best Actor Oscar to when he won for As Good as It Gets (1997).
- Son-in-law of Cab Calloway.
- Jack Nicholson wanted his old friend Rupert to play opposite him in The Last Detail (1973) as the sailor Mulhall, but Crosse was terminally ill and could no longer work. The part was played by Otis Young in the film.
- Studied acting under John Cassavetes.
- Worked at Brooklyn College as a counselor.
- Was brought up by his grandparents on the West Indies island of Nevis.
- Was a life member of The Actors Studio.
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