Truth be told, I almost didn't post my list because I'm kind of bummed that a couple of people chose not to watch my movie. I understand that it's not a top-ranked movie, and it was a little hard to find, but I made sure that it was available before nominating it, (on Amazon, on iTunes, on a couple of online sites, and it even aired on TCM during the HoF). I can watch the movies without joining the HoF, but the whole point of joining these HoFs is for people to watch your movie, so it's disappointing when people choose not to watch it.
Now that I got that off my chest, this is my ranked list. I based my ranking on how much I liked the movies, and I ignored the whole issue of whether or not they were "essential" movies.
1) Witness for the Prosecution (Billy Wilder, 1958)
2) The Gazebo (George Marshall, 1959)
3) High Noon (Fred Zinnemann, 1952)
4) The Man Who Knew Too Much (Alfred Hitchcock, 1956)
5) Ace in the Hole (Billy Wilder, 1951)
6) Wild Strawberries (Ingmar Bergman, 1957)
7) Ikiru (Akira Kurosawa, 1952)
8) La Strada (Federico Fellini, 1954)
9) Stage Fright (Alfred Hitchcock, 1950)
10) Caged! (John Cromwell, 1950)
11) Smiles of a Summer Night (Ingmar Bergman, 1955)
12) Rashomon (Akira, Kurosawa, 1950)
13) Twenty-Four Eyes (Keisuke Kinoshita, 1954)