Here's an interesting one:
John Cazale (Fredo from The Godfather). From Wikipedia "He appeared in five films over seven years, all of which were nominated for the Academy Award for Best Picture: The Godfather (1972), The Conversation (1974), The Godfather Part II (1974), Dog Day Afternoon (1975), and The Deer Hunter (1978), with the two Godfather films and The Deer Hunter winning. "
Are you notable if ALL your movies were nominated for Best Picture, even though you're not the main lead?
None of those characters are cops.