This is sort of stupid because if you only watched one movie every year you'd be missing out on some of the best movies of all time, also, a year can have 10 better movie than the following year so its all a bit pointless, anyways, if you really must make sure you watch these ones:
1919 - Broken Blossoms
1920 - The Cabinet of Dr. Caligari
1921 - The Phantom Carriage
1922 - Nosferatu
1923 - Safety Last!
1924 - Greed
1925 - The Gold Rush
1926 - Faust
1927 - Sunrise: A Song of Two Humans
1928 - Passion of Jean d'Arc
1929 - Un Chian Andalou
1930 - All Quiet on Western Front
1931 - M
1932 - Freaks
1933 - King Kong
1934 - It Happened One Night
1935 - Top Hat
1936 - Modern Times
1937 - Snow White and the Seven Dwarves
1938 - Bringing Up Baby
1939 - The Wizard of Oz
1940 - The Philadelphia Story
1941 - Citizen Kane
1942 - Casablanca
1943 - Shadow of a Doubt
1944 - Double Idemnity
1945 - Brief Encounter
1946 - It's a Wonderful Life
1947 - Out of the Past
1948 - Ladri di Biciclette
1949 - The Third Man
1950 - Sunset Blvd.
1951 - A Streetcar Named Desire
1952 - Singing in the Rain
1953 - Tokyo Story
1954 - Seven Samurai
1955 - The Night of the Hunter
1956 - The Searchers
1957 - Le Notti Bianchi
1958 - Touch of Evil
1959 - North by Northwest
1960 - L'Avventura
1961 - Last Year at Marienbad
1962 - Lawrence of Arabia
1963 - 8 1/2
1964 - Band à Part
1965 - Pierre Le Fou
1966 - Andrey Rublyov
1967 - The Jungle Book
1968 - Once Upon a Time in the West
1969 - Butch Cassidy and the Sundance Kid
1970 - Le Cercle Rouge
1971 - Harold and Maude
1972 - The Godfather
1973 - El Espíritu de la Colmena
1974 - Chinatown
1975 - One Flew Over the Cuckoos Nes
1976 - Network
1977 - Annie Hall
1978 - The Deer Hunter
1979 - Manhattan
1980 - StarWars Episode V: The Empire Strikes Back
1981 - Indiana Jones and the Raiders of the Lost Ark
1982 - Blade Runner
1983 - Sans Soleil
1984 - Paris, Texas
1985 - Brazil
1986 - Stand By Me
1987 - The Princess Bride
1988 - Nuovo Cinema Paradiso
1989 - Dekalog
1990 - Goodfellas
1991 - Beauty and the Beast
1992 - Reservoir Dogs
1993 - The Schindler's List
1994 - The Shawshank Redemption
1995 - Se7en
1996 - Fargo
1997 - LA Confidential
1998 - The Big Lebowski
1999 - Fight Club
2000 - Almost Famous
2001 - LotR: Fellowship of the Ring
2002 - Cidade de Deus
2003 - LotR: Return of the King
2004 - A Love Song For Bobby Long
2005 - Brick
2006 - El Labirinto del Fauno
2007 - The Assassination of Jesse James by the Coward Robert Ford
2008 - Martyrs
2009 - Inglorious Basterds
Just out of curiosity: the hardest years to decide, mostly because two (or more) of my favourite movies of all time were in them, were:
1968 - Once Upon a Time in the West over 2001: A Space Odyssey
1980 - Empire Strikes Back over The Shining
1985 - Brazil over The Goonies
1990 - Goodfellas over Edward Scissorhands
1993 - The Schindler's List over Jurassic Park
1994 - The Shawshank Redemption over the Lion King
1995 - Se7en over Toy Story
1998 - The Big Lebowski over American History X and Saving Private Ryan
2002 - Cidade de Deus over Road to Perdition
2004 - A Love Song for Bobby Long over Garden State, A Very Long Engagement and Eternal Sunshine of the Spotless Mind
2007 - The Assassination of Jesse James over Into the Wild
2008 - Martyrs over The Dark Knight