In fact, quite a few of them are Asian films that I've acquired through 'other means' so can't post them here. A few examples of films I like include:
A Better Tomorrow
Bad Lieutenant
Barry Lyndon
Betty Blue
The Beyond
Blue Velvet
Braindead
Casino
Christmas in August
Cinema Paradiso
City on Fire
Come and See
Class of 1984
Day of the Dead
Drop Dead Fred
The Football Factory
Get Carter
The God of Cookery
GoodFellas
The Good, the Bad and the Ugly
Hard-Boiled
The Hitcher
Hitch-Hike
House on the Edge of the Park
The Killer
La Haine
The Last House on the Left
Lilya 4-Ever
Lolita (the Adrian Lyne version)
The Magdalene Sisters
Maniac
The Man Without a Past
My Sassy Girl
Oasis
RoboCop
Saw
Scarface
Sexy Beast
Shaolin Soccer
The Straight Story
Straw Dogs
They Call Me Trinity
Trinity Is Still My Name
Zombi 2
...and I think that covers most of them.