Simply put, I enjoy watching movies. Below I list some of my favourite non-Hollywood, non-Indian movies:

Andrei Tarkovsky
There is this ethereal quality to his films. Almost like poetry in celluloid. And quite often, like poetry, very obscure and yet enjoyable.
Favourites: Solyaris, Mirror, Stalker
Nostalghia, The Sacrifice, My Name is Ivan

Federico Fellini
Favourites: 8 1/2, La Dolce Vita
Amarcord

Ingmar Bergman
Favourites: Wild Strawberries, Seventh Seal, The Silence, Autumn Sonata
Persona, Smiles of a Summer Night

Akira Kurosawa
Favourites: Seven Samurai, Rashomon, Ikiru
Yojimbo, Kagemusha

Krystof Kieslowski
Favourites: Three Colors: Blue
Three Colors: Red, Three Colors: White

Francois Truffaut
Favourites: 400 Blows
Shoot the Piano Player

Jean Luc Goddard
Favourites: My Life to Live, Breathless, Band of Outsiders, Contempt
Masculin Feminin, Pierrot Le Fou

Vittorio De Sica
The ultimate neo-realist.
Favourites: Bicycle Thieves, Umberto D

Michaelangelo Antonioni
L'Avventura, Blowup

Pedro Almodovar
Favourites: All About My Mother, Talk to Her
Women on the Verge of a Nervous Breakdown

Luis Bunuel
Favourites: The Exterminating Angel
Viridiana, Los Olvidados, Belle de Jour, The Discreet Charm of the Bourgeoisie

Henri-Georges Clouzot
The Wages of Fear

Fritz Lang
Metropolis

Abbas Kiarostami
Interesting perspectives on death in these two movies.
Favourites: The Taste of Cherry, The Wind Will Carry Us
Closeup

Majid Majidi
Favourites: Children of Heaven

Wim Wenders
Favourites: Wings of Desire
Paris Texas

Jacques Demy
Favourites: The Umbrellas of Cherbourg (I never realized musicals could be so interesting before I saw this film)

Emir Kusturica
Unique imagination. Specially, in Underground the absurdity of the story was fascinating.
Favourites: Time of the Gypsies, Underground

Yasujiro Ozu
Favourites: Tokyo Story

Wong-Kar Wai
Favourites: In the Mood for Love
Ashes of Time

Yimou Zhang
The Road Home ranks as one of the most exquisite romantic movies I have ever seen.
Favourites: The Road Home

Werner Herzog
Favourites: Aguirre - Wrath of God

Claude Chabrol
Favourites: The Butcher
Story of Women

Roberto Rossellini
Favourites: Open City
Voyage in Italy

Andre Techine
My Favourite Season

Hiroshi Teshigahara
Favourites: Woman in the Dunes

Marco Bellocchio
Henry IV

Atom Egoyan
The Sweet Hereafter

Andrzej Wajda
A sincere portrait of Stalinist Poland in Man of Marble
Favourites: Man of Marble

Misc.
Das Boot (Wolfgang Petersen), Cinema Paradiso (Giuseppe Tornatore), The Shop on the Main Street (Jan Kadar, Elmar Klos)