C

(x)The Earrings of Madame De . . . (1954)
(o)Cabaret (1972)
(x)The Caine Mutiny (1954)
(x)California Suite (1978)
(x)Calle 54 (2000)
(o)Camelot (1967)
(x)Camille (1937)
(x)Captains Courageous (1937)
(x)Carmen Jones (1954)
(x)Carnal Knowledge (1971)
(o)Casablanca (1942)
(x)Cat on a Hot Tin Roof (1958)
(x)Catch-22 (1970) [I started reading the book ages ago, but never got past page 94.]
(x)Cavalcade (1933)
(x)The Celebration (1998)
(x)La Cérémonie (1996)
(x)Chan Is Missing (1982)
(o)Chariots of Fire (1981)
(x)Charley Varrick (1973)
(o)Chicago (2002)
(o)Chicken Run (2000)
(x)La Chienne (1931, reviewed 1975)
(x)Chinatown (1974)
(x)Chloë in the Afternoon (1972)
(x)Chocolat (1988, reviewed 1989)
(x)The Cider House Rules (1999)
(x)The Citadel (1938)
(o)Citizen Kane (1941)
(x)Claire's Knee (1971)
(x)The Clockmaker (1973, reviewed 1976)
(o)A Clockwork Orange (1971)
(o)Close Encounters of the Third Kind (1977)
(x)Close-Up (1990, reviewed 1999)
(o)Clueless (1995)
(x)Coal Miner's Daughter (1980)
(x)The Color of Money (1986)
(x)Come Back, Little Sheba (1952)
(x)Coming Home (1978)
(x)The Conformist (1970)
(x)The Conquest of Everest (1953)
(x)Contempt (1964)
(x)The Conversation (1974)
(x)Cool Hand Luke (1967)
(x)The Count of Monte Cristo (1934) [I saw the 2002 remake...]
(x)The Country Girl (1954)
(x)The Cousins (1959)
(x)The Cranes Are Flying (1960)
(x)Cries and Whispers (1972)
(x)Crossfire (1947)
(x)Crumb (1994)
(x)Cry, the Beloved Country (1952)
(x)The Crying Game (1992)

I have seen 8/53 movies that start with the letter C.