Considering I don't watch a ton of movies, I'm going to be super lame and say Café Seagull.
It's about a Japanese woman running a café in Finland, and she's joined by two other Japanese women and a Finnish student who speaks Japanese. Sounds ordinary enough. Well, for a film who's supposedly somewhat rooted in reality, a ton of stuff happens in it which makes no sense.
Examples:
One of the Japanese women go out into the forest to pick mushrooms- and then they all disappear with no explanation.
Her lost luggage, which she needs to go home to Japan, is later found - and instead of it being full of her belongings, it's full of her goddamn mushrooms.
While she's talking about a possible mix-up on the phone, a man with a cat, which we've seen throughout the movie, approaches her. Without saying anything, he hands over the cat to her...and just walks away, leaving both the woman and the audience awfully confused.
I know it's not nearly as strange as some of the other movies seen in this thread. And for a Japanese movie, it's incredibly ordinary in comparison to films like these. [http://www.cracked.com/blog/3-most-perverted-looking-japanese-movies-netflix-tested/] But it's the small, strange details in an otherwise ordinary movie which make it stand out to me.
