I also totally agree with LC about Magnolia. Love that movie. Can hardly get anyone else to watch it.
Leningrad Cowboys Go America. This movie is hilarious in a wonderfully relaxed, totally deadpan way. Most people hate that. . .“it’s boring as hell.”
The Hitcher - I love this lightly-regarded slasher film. To me it is a brilliant study of a killer with a split personality. (Ryder ain’t real, IMO.) Nobody else seems to see it this way, or to enjoy the film like I did.
Same sorta deal with Runaway Train (Eric Roberts and John Voight.) I love the movie as a metaphor, but a lot of people just see two stupid cons on a train.
Gattaca. Some don’t like it because it doesn’t have a lot of high-tech gadgets given its future setting, but what gets to me is the story. I have sympathy for Ethan Hawke’s character.
Plunkett and Macleane. Most of the people I know have never even seen it; those who have didn’t like it. I love it.
Troop Beverly Hills
Phyllis: Oh, what glorious patches!
Jamie: Thank you, ma’am.
Phyllis: Where can I buy them?
Cleo: Ma’am, you don’t buy them, you earn them.
Phyllis: Oh! Like jewelry!
Twelfth Night
1996 - Trevor Nunn’s version with his wife, Imogen Stubbs, playing the lead, and the film is enticingly homoerotic. Richrd E. Grant and Ben Kingsley are brilliant, and it is the only Helena Bonham Carter role I can stand. The whole movie is understated, sweet, and hilarious.
Joe vs. the Volcano (already mentioned) shares the same pirate tape as Harold & Maude and Shirley Valentine. I watch this tape nonstop in its entirety. Everything is fine.
Brazil (found in Comedy, Drama or Horror section of any given video shop (any category is correct–which is why nobody else gets the movie)
Blade Runner – no one else seems to be as concerned as I am about what this story means if you have LARGE chunks of missing memories.
This was the first movie I thought of when I read the thread title. I love The Big Hit unreservedly – it’s campy and doesn’t take itself at all seriously. Cracks me up.
Also Super Troopers. Funnier than it has any right to be. And very few of my friends find it as hysterical as I do.
I’ll second The Mosquito Coast, and throw in my absolute favorite movie of all time, Rosencrantz & Guildenstern are Dead. Lately I’ve been compulsively checking for the release of this excellent Roth / Oldman flick on DVD. I probably shouldn’t regulate my breathing.
I showed Bottle Rocket to some of my friends one time. Some of them thought it was boring! 
The previously mentioned Magnolia and Punch-Drunk Love.
I’m the only person I know who thinks that ‘The Adventures of Buckaroo Banzai Through the Eighth Dimension’ is absolutely brilliant, but I know that one’s not exactly obscure by Dope standards.
Some of these I understand, but others are classics. Brazil, Rosencrantz & Guildenstern are Dead, Blade Runner, and Gattaca are all pretty well-appreciated amongst the folks I know.
Dread Pirate, you now know one other person who enjoyed Cutthroat Island. Goofy silliness, sure, but I had fun at it.
Daniel
The Three Amigos - I’m not even sure why I like it… but damn, it’s pretty funny.
Lucky Day: I suppose you could say that everyone has an El Guapo. For some, shyness may be an El Guapo. For others, lack of education may be an El Guapo. But for us, El Guapo is a large ugly man who wants to kill us!
The ones I was going to say have been mentioned, namely as Rosencrantz & Guildenstern are Dead and Magnolia.
I’ll also throw in Gerry, directed by Gus Van Sant, starring Casey Affleck and Matt Damon. The only thing is, I can’t really know if nobody else gets it the same way as me until I find a few more people who have even seen it. Also, nobody thinks I Spy is funny except my brothers and I.
vl_mungo,
I’m glad you mentioned this one, forgot all about it. I know a pile of people who think this one’s funny, including myself. I’m gonna go out and rent it tonight!
Three of John Boorman’s films:
Excalibur: One of the best examples of mythology on film.
Exorcist II: The Heretic: A dazzling meditation on the nature of Good and Evil and a journey into the collective unconscious.
Zardoz: A hilarious sendup of sci-fi cliches and intellectual elitism.
I’m in agreement with FisherQueen about Buckaroo Bonzai. It’s my favorite stupid movie; has a great cast doing really goofy stuff.
My other favorite is The Assasination Bureau, a late 60s’ comedy with Oliver Reed and Diana Rigg. It can’t be explained; it has to be seen.
Contact. I’d bet more Dopers actually appreciate that movie, though. Everyone wanted it to be about aliens.
What the movie actually DID demonstrate is that belief is, at its core, a function of the heart, figuratively speaking. A fantastic movie, I’d say.
Ditto to Twelfth Night, Brazil, Excalibur, and Buckaroo Banzai
but at this time of year, I have to bring out White Christmas. I cry when they sing “We’ll follow the old man” at the end. I love this movie!!! Hubby thinks I’m nuts.
Given this board I should just say everything Disney has put out lately…
but no a lot of it is crap…
A.I. Artificial Intelligence. Many hated it. I’ve always loved it. I think the movie is about a lot more than it seems.
The previously mentioned Magnolia and Gattaca.
Many people that I’ve mentioned The Fisher King to don’t seem to “get it”, either. That’s another movie I like quite a bit.
Mars Attacks!
Ack, Ack, Ack!