In addition to the movies and TV shows mentioned earlier, I would add:
NOTORIOUS (Hitchcock and Narzis, as Churchill pronounced the word according to Mel Brooks)
"BACK THERE" (Twilight Zone episode where Russell Johnson goes back in time to try to stop the assassination of Lincoln)
EXECUTIVE ACTION (Way before Oliver Stone's "JFK")
JFK (Love to see Joe Pesci as David Ferrie!)
NIXON (Love to see the scenery chewing)
SECRET HONOR (Great acting by Philip Baker Hall as Nixon, later Lt. Bookman on "Seinfeld")
THE IPCRESS FILE (More conspiracy with a British version of MK-ULTRA and Michael Caine)
FUNERAL IN BERLIN (More Michael Caine)
MARATHON MAN (Olivier as a Nazi dentist, "Is it safe?" and no novocaine for Dustin Hoffman)
THE BOYS FROM BRAZIL (Olivier as a Simon Wiesenthal Nazi hunter)
NETWORK (Faye Dunaway as a TV news producer trying to get inside a Patty Hearst-style terror group)
THE PARALLAX VIEW (Warren Beatty peels away the political conspiracy onion and doesn't like what he finds)
REDS (Warren Beatty! Nicholson is extremely good as Eugene O'Neill)
ANIMAL FARM (Animated, yes, but still scary)
ONCE UPON A TIME IN THE WEST (The Old West filtered through the politics of 1960s Italy)
OUR MAN IN HAVANA (Both the book by Greene and the movie with Alec Guinness, satirical thriller)
JULIUS CAESAR (The Mankiewicz version with Marlo Brandon [that's the way my mom said it, so I'm sticking with it])
WR: MYSTERIES OF THE ORGANISM (Wilhelm Reich!)
THE PRIVATE FILES OF J. EDGAR HOOVER (Fun Larry Cohen TV movie with Broderick Crawford as Hoover bulldozing!)