The veteran character actor, who starred in films including Kill Bill Vol 1 and 2, Argo and Red State, died on Tuesday morning, his agent Jane Schulman said.
Parks worked alongside directors such as Quentin Tarantino, Robert Rodriguez and Kevin Smith on the big screen.
But he is perhaps best known for his role as Canadian drug runner Jean Renault in David Lynch's 1990s cult TV series Twin Peaks.
Parks' death comes just weeks before a Twin Peaks reboot, set 25 years after the original, is aired on Showtime in the US and on Sky Atlantic in UK. Parks did not appear in the new series.
Smith, who was a close friend, described him as "the best actor I've ever known".
Writing on Instagram, he added: "He was, hands-down, the most incredible thespian I ever had the pleasure to watch perform."
Ms Schulman described him as the "greatest living actor".
Parks was born in April 1940 in Corona, California, the son of a baseball player.
He played roles in TV shows including Perry Mason and Dynasty, and later enjoyed a number of film parts in From Dusk Till Dawn, Red State and Tusk.
He is survived by his wife, Oriana, and son James.
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