Great movies to screw with your head

I love movies that don't reveal exactly what's going on all the time, and allow for a bit (or a lot) of audience interpretation. Here I've got things from relatively mild craziness or film with wacky timelines, to complete WTF-ness. The thing they all have in common is that they're fun to figure out!
(Not in any particular order)
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1.
Black Swan (2010)
    1 2 3 4 5 6 7 8 9 10 8.0/10 X  
A committed dancer wins the lead role in a production of Tchaikovsky's "Swan Lake" only to find herself struggling to maintain her sanity. (108 mins.)
“ What is actually happening, and what is just a hallucination? Fairly simple to work out, but an amazing movie! ” - leturtle
 
2.
Eternal Sunshine of the Spotless Mind (2004)
    1 2 3 4 5 6 7 8 9 10 8.3/10 X  
When their relationship turns sour, a couple undergoes a procedure to have each other erased from their memories. But it is only through the process of loss that they discover what they had to begin with. (108 mins.)
Director: Michel Gondry
“ We've got reality, and then we've got the memories of our protagonist- shown to us in reverse order as they are deleted. ” - leturtle
 
3.
The Prestige (2006)
    1 2 3 4 5 6 7 8 9 10 8.5/10 X  
Two stage magicians engage in competitive one-upmanship in an attempt to create the ultimate stage illusion. (130 mins.)
“ Again, not hard to work out if you concentrate, but the crazy timeline confused the hell out of me the first time I saw this. Nolan's best and most underrated movie to date. ” - leturtle
 
4.
Inception (2010)
    1 2 3 4 5 6 7 8 9 10 8.8/10 X  
A thief, who steals corporate secrets through use of dream-sharing technology, is given the inverse task of planting an idea into the mind of a CEO. (148 mins.)
“ Might cop some flaming with the above comment on The Prestige, so I should add this to the list just in case! ” - leturtle
 
5.
Memento (2000)
    1 2 3 4 5 6 7 8 9 10 8.5/10 X  
A man juggles searching for his wife's murderer and keeping his short-term memory loss from being an obstacle. (113 mins.)
“ Most of Nolan's films could qualify for this list, but they're all brilliant in their own way. How many movies do you see that are shown in backwards order?? ” - leturtle
 
6.
Mulholland Dr. (2001)
    1 2 3 4 5 6 7 8 9 10 8.0/10 X  
After a car wreck on the winding Mulholland Drive renders a woman amnesiac, she and a perky Hollywood-hopeful search for clues and answers across Los Angeles in a twisting venture beyond dreams and reality. (147 mins.)
Director: David Lynch
“ Easily a 10/10 on the WTF scale. Lynch, you insane genius. ” - leturtle
 
7.
Fight Club (1999)
    1 2 3 4 5 6 7 8 9 10 8.8/10 X  
An insomniac office worker, looking for a way to change his life, crosses paths with a devil-may-care soap maker, forming an underground fight club that evolves into something much, much more. (139 mins.)
Director: David Fincher
“ Much more philosophical and complex than the title would have you expect. ” - leturtle
 
8.
Donnie Darko (2001)
    1 2 3 4 5 6 7 8 9 10 8.1/10 X  
A troubled teenager is plagued by visions of a man in a large rabbit suit who manipulates him to commit a series of crimes, after he narrowly escapes a bizarre accident. (113 mins.)
Director: Richard Kelly
“ I'm not even sure if the writer/director knows entirely what's going on here, but the ending will leave you floored no matter how little you understand it. Gets better everytime I watch it. ” - leturtle
 
9.
The Shining (1980)
    1 2 3 4 5 6 7 8 9 10 8.4/10 X  
A family heads to an isolated hotel for the winter where an evil and spiritual presence influences the father into violence, while his psychic son sees horrific forebodings from the past and of the future. (146 mins.)
Director: Stanley Kubrick
“ The next three are all Kubrick films, and all wonderful mind screws! This one is damn scary with an amazing performance by Jack Nicholson. ” - leturtle
 
10.
2001: A Space Odyssey (1968)
    1 2 3 4 5 6 7 8 9 10 8.3/10 X  
Humanity finds a mysterious, obviously artificial object buried beneath the Lunar surface and, with the intelligent computer H.A.L. 9000, sets off on a quest. (149 mins.)
Director: Stanley Kubrick
“ Evolutionary sci-fi crosses over with art crosses over with LSD trip. ” - leturtle
 
11.
A Clockwork Orange (1971)
    1 2 3 4 5 6 7 8 9 10 8.3/10 X  
In future Britain, Alex DeLarge, a charismatic and psycopath delinquent, who likes to practice crimes and ultra-violence with his gang, is jailed and volunteers for an experimental aversion therapy developed by the government in an effort to solve society's crime problem - but not all goes according to plan. (136 mins.)
Director: Stanley Kubrick
“ Probably the most clear-cut of these three Kubrick films I've chosen, but it's still pretty bizarre (in the most awesome way possible!) ” - leturtle
 
12.
Spirited Away (2001)
    1 2 3 4 5 6 7 8 9 10 8.6/10 X  
During her family's move to the suburbs, a sullen 10-year-old girl wanders into a world ruled by gods, witches, and spirits, and where humans are changed into beasts. (125 mins.)
Director: Hayao Miyazaki
“ One of the few films on this list I'd happily show to a child. One of my favourite movies ever, and takes quite some thought to work out exactly what's going on. And yet suitable for all ages to enjoy. ” - leturtle
 
13.
Pan's Labyrinth (2006)
    1 2 3 4 5 6 7 8 9 10 8.2/10 X  
In the falangist Spain of 1944, the bookish young stepdaughter of a sadistic army officer escapes into an eerie but captivating fantasy world. (118 mins.)
“ Not so much with the main storyline, but the ending leaves some ambiguity as to whether everything we've just seen is real or just a child's imagination. ” - leturtle
 
14.
Sucker Punch (2011)
    1 2 3 4 5 6 7 8 9 10 6.1/10 X  
A young girl is institutionalized by her abusive stepfather, retreating to an alternative reality as a coping strategy, envisioning a plan to help her escape. (110 mins.)
Director: Zack Snyder
“ I beg of everyone, give this movie a chance! So much more than just the mindless action fluff it's being advertised as. Though that may have been Snyder's point all along... ” - leturtle
 
15.
Saw IV (2007)
    1 2 3 4 5 6 7 8 9 10 5.9/10 X  
Despite Jigsaw's death, and in order to save the lives of two of his colleagues, Lieutenant Rigg is forced to take part in a new game, which promises to test him to the limit. (93 mins.)
“ The whole series would easily qualify for this list, and while Saw IV might not be the best one, it certainly is the most mind-screwy! ” - leturtle
 
16.
The Triplets of Belleville (2003)
    1 2 3 4 5 6 7 8 9 10 7.8/10 X  
When her grandson is kidnapped during the Tour de France, Madame Souza and her beloved pooch Bruno team up with the Belleville Sisters--an aged song-and-dance team from the days of Fred Astaire--to rescue him. (78 mins.)
Director: Sylvain Chomet
“ I could watch this .over and over again. Main WTF-ness is in... why are the mafia kidnapping cyclists? Surely for more reason that to just bet on them racing on a bizarre bike machine..... right? Wonderful animation. ” - leturtle
 
17.
Citizen Dog (2004)
    1 2 3 4 5 6 7 8 9 10 7.5/10 X  
Pod is a man without a dream. He's a country bumpkin who comes to work at a tinned sardine factory in Bangkok... (100 mins.)
“ The storyline itself is pretty easy to follow, but it's just so freaking bizarre that I actually wondered if I had dreamt the whole thing! A talking teddy bear, a chain-smoking 20-year-old stuck in a 9-year-old's body, a lizard with the face of an old human woman, a giant pile of plastic bottles that REACHES THE MOON... surely only something like that could be manifested in some unstable dream world? But no, this movie definitely exists, and it's amazing. ” - leturtle
 
18.
Shutter Island (2010)
    1 2 3 4 5 6 7 8 9 10 8.1/10 X  
In 1954, a U.S. marshal investigates the disappearance of a murderess who escaped from a hospital for the criminally insane. (138 mins.)
Director: Martin Scorsese
“ Everything is explained in the end, but a great movie that keeps you questioning the whole time. ” - leturtle
 
19.
Paranoia Agent (2004 TV Series)
    1 2 3 4 5 6 7 8 9 10 8.2/10 X  
Seemingly unconnected citizens of Tokyo are targeted for bludgeoning by a boy with a golden baseball bat. As detectives try to link the victims, they discover that following the assaults, the victims' lives have improved in some way. (30 mins.)
“ This is more of an honorary mention, because it's not a movie but an 11-episode anime series. But it fills in all the criteria I mentioned above, and is bloody brilliant! ” - leturtle