In 1960, he married Ida Hove, who survived him, along with three sons, Stefan, John and Andrew Prosky. Andrew and John Prosky are also actors.

In addition to his film and television career, he appeared in numerous productions at the Arena Stage in Washington, D.C., most notably as Willy Loman in Death of a Salesman. Prosky often performed at Arena Stage with over 100 stage credits to his name at that theatre alone. He played Shelly Levene in the 1984 Chicago and Broadway production of David Mamet's Pulitzer Prize-winning play Glengarry Glen Ross. He was also a board member of the Cape May Stage in Cape May, New Jersey.

Prosky appeared in Thief, Christine, Hanky Panky, The Natural, Hoffa, Broadcast News, Things Change, The Great Outdoors, Loose Cannons, Rudy, Mrs. Doubtfire, Green Card, and Dead Man Walking. In addition to appearing in films, Prosky appeared as a regular on Hill Street Blues, Danny, and Veronica's Closet. He was considered for the role of Martin Crane in Frasier and later made a guest appearance in the series as a reclusive Writer. He portrayed Rebecca Howe's father on Cheers; on the same show, he was offered the role of Coach Ernie Pantusso, but turned it down. Prosky also portrayed Jake "the Snake" Connolly on a 2-part 1991 episode of Coach.

On December 8, 2008, Prosky died at age 77, 5 days before his 78th birthday. His son John said that the cause was complications of heart surgery at the Washington Hospital Center. He was survived by his wife, the former Ida Hove, an anthropologist; another son, Stefan, a microbiologist; and three grandchildren. The New York Times described him: "...a craggy-faced, heavyset character actor who after 23 years in regional theater became a familiar face on Broadway, in movies and on television, notably as a gruff desk sergeant in the later years of 'Hill Street Blues.'"