Hello,
Yes, I also quite like movies and watch a lot of them. I do prefer the ones that make you think or allow me to see something differently. Some classics, some cult, some rare, some indie, and some downright bizarre ones. I never bothered to list all of them though.
These are some of the ones I liked a few years ago: Pi, An American Crime, Duck! The Carbine High Massacre, Possible Worlds, the Cube trilogy, the Ginger Snaps Trilogy, A Beautiful Mind, The Fountain, the Hannibal series, Finally Equal (2081), The I Inside, Idiocracy, Blade Runner, Mr. Brooks, Pandorum, Cargo, Les Sept Jours du Talion (7 days), Das Parfum – Die Geschichte eines Mörders (Perfume: Story of a Murder), Der Kanibale Von Rothenburg (which I could never bring myself to watch to the end, it is quite sad and disturbing), Minority Report, The Secret Window, Zero Day, Stir of Echoes, Donnie Darko, Gataka, The Jacket, American Psycho 2, Pathology, Dread, Sweeney Todd, Antichrist (by Von Trier), Black Swan, The Cement Garden, The Cell, I Spit on Your Grave, A Clockwork Orange, Choke, Fight Club, Moon, Darkstar, The Village, The Butterfly effect (only the first), Hide and Seek, V for Vendetta, Equilibrium, 28 . . . Later, Cry Wolf, Pulse, Hackers, The Invisible, Stay Alive, the Crow series, The Devil's Rejects, the Underworld series, The Matrix trilogy (although the last Matrix movie was disappointing to say the least).
I have to add Synecdoch NY, Mona Lisa Smile, The last airbender, Girl Interrupted, Quills, Electric dreams, Cyrano de Bergerac, M. Butterfly, Naked, Reprise, Mozart and the Whale, Les amities particulieres, Let the right one in, The secret world of words, 2081 Finally equal, Sunshine, Solaris, Agora, The life of Brian, Dark Matter, Being John Malcovich, Heathers (Mean girls but psychotic), Moon, Boys Don't cry, Flat land, Harold and Maude and should stop myself and just make an IMDB list already.

Yes I am into really odd things and have a soft spot for dark comedies and stories that are just plain strange and normally disturbing to everyone but me. Go figure.