Kirk Douglas sought Corey's advice about playing the title role in Spartacus (1960).
Children: daughters Eve, Jane, Emily.
Served in the Navy during World War II.
When he was summoned to a hearing of the House Un-American Activities Committee, he not only refused to name names but also offered an acting critique of the previous witness. He was promptly blacklisted and did not work in films or television for 12 years.