I am listing some offbeat movies which I assume, very few members on this thread must have watched. These won't match everyone's taste but of a selected few. Do give them a try at your leisure. I have mentioned them earlier but they must be dispersed in this thread which has become so vast!
Before Sunset- Maybe most of you have already seen it. But this one is not to be missed. Only 2 characters with wonderful chemistry.
Chasing Amy- One of the most complex movies on relationships.
Closer-Watch out for the opening track. A movie on screwed relationships.
Dear Frankie-Senti movie starring Gerard Butler.
In Bruges-Different ganster movie with some good humor. Great acting by the leads.
Sublime - A good medical thriller with a little mindfcuk.
The Fall- Visually stunning. You must have never seen India so beautifully captured by Tarsem Singh. Another good movie by him after The Cell. Also watch out for the small girl who has acted wonderfully.
The Skeleton Key - Good thriller with a twist.
Let the right one in - Vampire love story. Arguably the best Vampire movie out there.
Departures - The Oscar winner from Japan. I really wonder how they bring such wonderful scripts out of nowhere. A must watch.
The Broken - A bit slow but amazing movie about the clones (?Doppelganger)
Case 39 - Horror movie. Worth a watch.
Tulpan - Kazakh movie. A movie about survival with subtle humor. A must watch.
Dog Soldiers - From the director of ? The Descent. Good British horror.
Ikigami - Great script. Only Japanese can make such movies. A must watch.
Spider Forest - David Lynch type brainfcuk movie. Amazing direction. A must watch.
Triangle - Similar description as above. A must watch.
Matrubhoomi: A nation without women - A movie set in futuristic village in Bihar where there are no women left due to infanticide. A unique movie from bollywood.
Hazaaron Khwaishein Aisi - Another great bollywood product by Sudhir Mishra. Great acting by Shiney Ahuja, Chitrangada Singh and Kay Kay.
Beerfest - Good timepass comedy.
Clerks- Good humor. A movie by Kevin Smith.
Black Water - A movie on a croc attach. Very effectively made.
Stay - Another brainfcuk movie.
The Tape - Shot in a single room with 3 characters. Great acting.
Marathon - I started watching Asian movies with this one. Great direction and acting.
Dancer in the dark - This movie will break your heart.
Away from her - If you loved Notebook, you will love this even more.
Chupke se - Offbeat comedy from bollywood which went unnoticed.
Into the wild - True story of a man who gave up all to go to Alaska. One of the best soundtracks. A must watch.
Sita Sings The Blues - Animated movie by Nina Paley. A must watch. Available free for download on the director's website.
Solaris - A bit slow but great psychological movie set on the spaceship Solaris. George Clooney.
The Beach - Different story starring Leonardo.
The Lake House - Hollywood remake of the korean movie Il Mare.
The Fountain - Another masterpiece from the director of Requiem for the dream. Awesome soundtrack.
The Hamiltons - B grade horror movie from the horrorfest few years back. A good watch.
Gunda - Mother of all Indian movies. Was highest rated Indian movie on imdb not too long ago. Directed by none other than Kanti Shah with unique and mindblowing(literally) script by Bashir Baber. Highly recommended.
There must be many more. I have a feeling I have left out many Asian, Spanish and French movies. But these are the ones I could recall as on today.