Even though I love Asian cinema. There are only two that are favourites.
Most of my favourites are in the english language, and a few in other languages
see
http://www.imdb.com/list/ls000065201/

I really can't come up with my own list.

Moment of Peace-

My favourite non-Asian films ordered by year.
I marked the Indian films with
I
because - though for me those are Asian films - most here would count them as non-Asian:
Nosferatu, eine Symphonie des Grauens (1922)

• F.W. Murnau
  Metropolis (1927)
• Fritz Lang
  Aleksandr Nevskiy (1938)
• S. Eisenstein, D. Vasilyev
  The Philadelphia Story (1940)
• George Cukor
  Ivan Groznyy (1945)
• Sergei Eisenstein
  La belle et la bête (1946)
• Jean Cocteau
  I
  Pather Panchali (1955)
• Satyajit Ray
  12 Angry Men (1957)
• Sidney Lumet
  Det sjunde inseglet (1957)
  The Seventh Seal
• Ingmar Bergman
  Cat on a Hot Tin Roof (1958)
• Richard Brooks
  I
  Apur Sansar (1959)
  The World of Apu
• Satyajit Ray
  North by Northwest (1959)
• Alfred Hitchcock
  Who's Afraid of Virginia Woolf? (1966)
• Mike Nichols
  2001: A Space Odyssey (1968)
• Stanley Kubrick
  The Lion in Winter (1968)
• Anthony Harvey
  Alien (1979)
• Ridley Scott
  Das Boot (1981)
• Wolfgang Petersen
  The Abyss (1989)
• James Cameron
  When Harry Met Sally (1989)
• Rob Reiner
  Strictly Ballroom (1992)
• Baz Luhrmann
  Groundhog Day (1993)
• Harold Ramis
  I
  Bandit Queen (1994)
• Shekhar Kapur
  I
  Koyla (1997)
• Rakesh Roshan
  I
  Theeviravaathi: The Terrorist (1998)
• Santosh Sivan
  I
  Asoka (2001)
  Ashoka the Great
• Santosh Sivan
  Enigma (2001)
• Michael Apted
  Black Hawk Down (2001)
• Ridley Scott
  I
  Satta (2003)
• Madhur Bhandarkar
  Dear Frankie (2004)
• Shona Auerbach
  The Phantom of the Opera (2004)
• Joel Schumacher
  The Fountain (2006)
• Darren Aronofsky
  Prince of Persia: The Sands of Time (2010)
• Mike Newell
  each brain develops its own preferences

Suspiria used to be my favourite horror film in highschool, I should watch it again someday.

Favourite films:
http://www.imdb.com/list/ls006514680/

Some of my favorites (in chronological order):
Sherlock Jr. (1924, US)
Metropolis (1927, Germany)
The Cranes Are Flying (1957, Soviet Union)
Dr. Strangelove (1964, US)
Happy End (1967, Czechoslovakia)
Birds, Orphans and Fools (1969, Czechoslovakia)
The Mother and the Whore (1973, France)
The Fifth Seal (1976, Hungary)
Perfumed Nightmare (1977, Philippines)
Suspiria (1977, Italy)
Arrebato (1979, Spain)
The Story of the Voyages (1983, Soviet Union)
Close-Up (1990, Iran)
My Winnipeg (2007, Canada)

Withnail & I (1987)
Taxi Driver (1976)
Jean De Florette / Manon Des Sources (1986)
The Thin Red Line (1998)
Three Colours: Blue (1993)
Alien (1979)
Pulp Fiction (1994)
Walkabout (1971)
Deliverance (1972)
A Clockwork Orange (1971)
Last Film Seen;
The Wailing
(Na Hong-jin, 2016)
7/10

These are all great lists from you guys.
-Apocalypse Now (It's not a 10, it's about a 17)
-2001 A Space Odyssey
-La Cienaga
-The Act of Killing
-8 1/2
-4 Months, 3 Weeks, and 2 Days
-Lawrence of Arabia
I have to subtract 2046 and Oasis from my list of 10s on the basis of being Asian.
If I had to fill the top 10 out with 9s, I would probably pick from:
-La Dolce Vita
-Bridge on the River Kwai
-Underground (1995)
-Wild Strawberries
-Fitzcarraldo
-Talk to Her
-Marilena from P7
-Rear Window
-Y Tu Mama Tambien
-Das Boot
-Solaris
-Mulholland Drive
-American Beauty
-Fargo
Interestingly, these are mostly sort of traditional arthouse movies. Although I do agree that Groundhog Day deserves a place in this list!

It's impossible to narrow down to 10, but I'll list some of my favorite dramas. I have not seen many non-Asian films released before 1970.
Heat
Glengarry Glen Ross
Goodfellas
The French Connection
All About Eve (1950)
V for Vendetta
Ben Hur (1959)
The Godfather 1 and 2
Rear Window
Dark City
YouTube Asian Movie Review Channel
https://www.youtube.com/user/anticlimacus100

At first blush that looked like a wacky list, then I put mine together. It's wacky, too!
Lost in Translation
used to have a place. I watched that film over a dozen times, but what's her face has soiled my enjoyment of it any more.
I think I used to think I liked
For A Few Dollars More
more than
The Good, the Bad and the Ugly
, but when I think of them now all the outstanding scenes come from the latter. One of them belongs on this list (probably in place of
Tombstone
) but since I can't decide which one without some re-watches, I'll just honorably mention them.
In chronological order:
All the President's Men

• (Alan J. Pakula, 1976)
  Apocalypse Now
• (Francis Ford Coppola, 1979)
  Jacob's Ladder
• (Adrian Lyne, 1990)
  Trust
• (Hal Hartley, 1990)
  Groundhog Day
• (Harold Ramis, 1993)
  Tombstone
• (George P. Cosmatos, 1993)
  The Spanish Prisoner
• (David Mamet, 1997)
  Mr. Jealousy
• (Noah Baumbach, 1997)
  Shakespeare in Love
• (John Madden, 1998)
  Eternal Sunshine Of The Spotless Mind
• (Michel Gondry, 2004)