After the first three or so it's really in no particular order (these are my favorite movies, not my choice for the best movies).

1. Kind Hearts and Coronets
2. Billy Liar!
3. Badlands
4. Double Indemnity
5. Duck Soup
6. Sherlock Jr.
7. The Godfather
8. Casablanca
9. North by Northwest
10. It's A Wonderful Life
11. Singin' In The Rain
12. Force Of Evil
13. Seven Samurai
14. Wizard of Oz
15. Peter Ibbetson (1936)
16. Sleuth (1972)
17. Hud
18. Orpheus (1949)
19. Sweet Smell Of Success
20. Hail The Conquering Hero

Note there are no westerns on my list. Last year I made up a separate list of my top 100 westerns.

Top 20:

Ride the High Country
The Tall T
3:10 to Yuma (1957)
Johnny Guitar
The Good, the Bad and the Ugly
Rio Conchos
The Searchers
Red River
Silver Lode
The Wild Bunch
The Man Who Shot Liberty Valance
Ride Lonesome
The Magnificent Seven
The Oklahoma Kid
One-Eyed Jacks
Man Without A Star
The War Wagon
The Man from Laramie
The Shooting
Son of Paleface

The Rest (in no particular order):
Fury At Showdown (1957)
The Day Of The Outlaw
Bend Of The River
Forty Guns
Hombre
Union Pacific
Law And Order (1932)
Cowboy
The Law And Jake Wade
Reprisal! (1956)
Apache Drums (1952)
The Big Sky
For a Few Dollars More
El Dorado
The Virginian (1929)
The Left Handed Gun
Dodge City
Silver River
Warlock
Texas (1941)
No Name On The Bullet
Flaming Star
Seven Men From Now
Shane
High Noon
Stagecoach
She Wore A Yellow Ribbon
Butch Cassidy & the Sundance Kid
The Far Country
The Shootist
The Big Silence
My Darling Clementine
Fort Apache
The Westerner
Winchester '73
Destry Rides Again
Will Penny
Bandolero
The Last Train from Gun Hill
A Fistful of Dollars
Broken Arrow
Man of the West
The Violent Men
The Naked Spur
They Died With Their Boots On
The Mark of Zorro
Gunfight at the O.K. Corral
Once Upon a Time in the West
The Big Trail
The Professionals
Blazing Saddles
Vera Cruz
The Unforgiven (1960)
Northwest Passage
Hour of the Gun
The Hanging Tree
The Big Country
Wells Fargo
The Plainsman
Escape from Fort Bravo
Pat Garrett and Billy the Kid
Cat Ballou
Hondo
The Last Hunt
Drums Along the Mohawk
The Iron Horse (1924)
Rio Grande
The Lone Ranger (1956)
The Comancheros
The Paleface
Support Your Local Sheriff
My Pal Trigger (1946)
The Great K&A Train Robbery (1926)
Tumbleweeds (1925)
The Great Train Robbery (1969)
Devil's Doorway
The Scalphunters
There Was a Crooked Man
Comanche Station
Day Of The Evil Gun
The Marauders
Gunman's Walk
Waterhole #3
The Assassination Of Jesse James By The Coward Robert Ford