Vincent's family said he died peacefully and surrounded by his loved ones. No cause of death was given.
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"We ask that you respect our privacy during this difficult time," a statement from the family said.
During his time on the HBO hit series, he played mob boss Phil Leotardo. Director Martin Scorsese hired Vincent for memorable roles in three movies: "Raging Bull," "Goodfellas" and "Casino."
Vincent also had small roles in two Spike Lee films, "Do the Right Thing" and "Jungle Fever," and also was in "The Pope of Greenwich Village," ''Last Exit to Brooklyn," ''Night Falls on Manhattan" and "Shark Tale," among his more than 50 movies.
The actor's career spanned 41 years and before that, he was an accomplished musician who played with Paul Anka, Trini Lopez and Del Shannon.
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Raised in Jersey City, New Jersey, he acted in school plays and learned piano, trumpet and drums.
In 1975, he made his feature film acting debut in Ralph DeVito's "Death Collector," where he was spotted by Scorsese.
In 2006, Vincent published "A Guy's Guide to Being a Man's Man."
The Associated Press contributed to this report.