I just thought of another one: the Taking of Pelham One Two Three.
First, I second the mentions of Noises Off and Me and You and Everyone We Know. Amazing movies.
And so is Primer. It’s a recent independent science fiction film about two guys who stumble on time travel. This movie, in my opinion, really goes back to the roots of what science fiction was (when it first arose), is (sometimes today), and should be: addressing the social/ethical/psychological implications of science and technology. It’s fantastically low budget - the entire thing was made for less than $7k, the acting is gritty and you feel like you’re watching real engineers go back and forth on this stuff. The plot, however, is a Gordian knot of different perspectives, repeated periods of time, codas on top of codas, and more. It’s a lot like the theory of relativity: if you think you understand it, you haven’t been paying attention.
I’ll add a couple more:
East Side Story. A documentary on communist musical films, including Stalin’s favorite, Volga, Volga and such classics as Tractor Drivers, Cossaks of the Kuban, My Wife Wants to Sing, and The Little White Mouse. And, no, I’m not putting you on – the films existed and you can see some amazing clips from them.
Targets – Boris Karloff as an old monster movie actor face-to-face with real-life horror.
A couple of my favorites have already been mentioned (The Frisco Kid, Don Juan de Marco), so that leaves me with:Dominick and Eugene . I haven’t seen it in ages, but it made me cry in a couple of places.
The Park is Mine, w/ Tommy Lee Jones
The Wizard of Mars w/iirc John Carradine
Attack of the Mushroom People
Panic in the Year Zero
Soapdish w/Sally Fields, Kevin Kline, R. Downey Jr.
I’ve seen it, and I’m surprised there’s even one person who has anything positive to say about it, let alone three.
This one I agree with. I wasn’t much older than the main character when I saw it, and it really plucked my heartstrings.
Cemetary Man aka Dellamorte Dellamore: Sci-Fi, Horror-Comedy-Satire. Rupert Everett and Anna Falchi. Wiki claims
The Navigator: Medieval time-travel road-movie/quest. An early New Zealand cinematic triumph.
A second vote for Tampopo.
Farewell My Concubine: On reading the Wiki article, this seems to be well known to the good folks at Cannes as well as 1,000,000,000 Chinese people. So it probably doesn’t really belong. Nobody I know seems to recall it though.
Hmmm…I’ve seen a lot of the movies mentioned, (They Live, Amazon Women on the Moon, Blood of Heroes, Buffalo '66, Pi) and while they are definitely obscure, and I did like them a lot, they aren’t close to being my favorites.
So based on that, I’ll offer:
Erik the Viking
Closet Land
Shallow Grave
The I Inside
Not my favorites, but quite obscure and I like them enough to buy the DVDs. (Though I haven’t yet.)
Gotta love the pro wrestling thumbs–“Nobody messes with POOP CHUTE!” I thought my poor daughter would die laughing!
I mentioned High Strung earlier–the star of that movie is the same man who makes all those Thumb shorts, Steve Oedekerk. I think the guy’s a riot!
Some of mine have already been mentioned but this is fun and i’ll repeat some:
I can’t BELIEVE Scavenger Hunt was brought up. I used to watch that when I was little.
**My Own Private Idaho
Pi
Tarnation
Desperate Living
Mondo Trasho
Walkabout
Salo
The Dreamers
Ripe
Buffalo 66 (although I think a lot of people have seen that)
Opposite of Sex (same)
Audition
Female Trouble
House of Yes
“Root’s kicking in!”
“Give me a tall glass of warm gin with a human hair in it.”
“We’re both Colonels.”
“Your horse is named Wildfire? My horse is named Wildfire!”
I’ll see you with:
The Little Girl Who Lives Down the Lane
Gregory’s Girl
Shock Treatment
Local Hero
Manhunter
and raise you with:
Bert Rigby, You’re a Fool
Carny (yes, I’ve got a Jody Foster thing going here)
heh, looking though my vote history at imdb, my favorites include Bob Roberts, Farewell My Concubine, Amazon Women on the Moon, and Ran.
Some others:
Uzumaki. Excellent horror movie. A little more cartoonish than Ringu, but much creepier. Even in Japan, nobody seems to have heard of it.
The Story of Qiu Ju. One of the lesser-known movies that Zhang Yimou and Gong Li did together. Kind of reminded me of one of Chekov’s stories.
The Rutles: All You Need is Cash. Brilliant Beatles parody.
The Quiet Earth is an excellent film, and Bruno Lawrence was huge in NZ in the late '70s and early '80s. He also had a band- Blerta (Bruno Lawrence’s Electric Revelation and Travelling Apparition), best known for the song “Dance All Around The World”.
OK, my favourite movies that hardly anyone seems to know of:
The Day Of The Jackal (1973). An absolutely perfect film version of one of my favourite books- indeed, I’d argue this film is the best “Film version of a Book” ever made. Not to be confused with the abomination made in 1997 starrting Bruce Willis.
Mystery Men (1999). A Brilliant spoof on Superhero Movies, with Ben Stiller as Mr. Furious (and, at the peak of his rage, can just about get the hood ornament of a limousine), William H. Macy as The Shoveller- who hits people with a shoveller- and Hank Azaria as The Blue Rajah, who throws cutlery at people. Brilliant and wholly under-rated, IMO.
Kung Pow: Enter The Fist (2002). What can I say? I have a weakness for appallingly dubbed Hong Kong Action Movies- and anything which takes the piss out of them. 
A Better Tomorrow II (1987)- John Woo, Chow Yun-Fat, plenty of gunfire. There’s also a vaguely coherent plot here, and the final shoot-out is very well done, too.
Hercules Returns (1993). Imagine a bunch of crazy Aussies ad-libbing and re-dubbing an old Italian Sword & Sandal epic, and you’ve got Hercules Returns. Quite possibly one of the funniest movies I’ve ever seen, and inexplicably not available on DVD.
There are medications available to assist you in living a normal life. Wait, maybe you’ve had too much medication. 
This is obscure? It was a major flick when it came out, from a major director (Fred Zinneman also gave us a Man for All Seasons and High Noon.) Heck, I just watched it last night.
I’m throwing in with a vote for Noises Off. I got to see the play in the early 80s and adored it, then spotted the video one day at Blockbuster. The cast includes Carol Burnett, Christopher Reeve (pre “I’m a 6’2” jockey!"), Marilu Henner (of Taxi), John Ritter, Martin Mull, Mark Linn-Baker (Perfect Strangers), Julie Hagerty (Airplane!), Michael Caine, Nicolette Sheridan (who I thought had dropped off the earth, and so I was stunned when I heard she was on Desperate Housewives), Denholm Elliot (Trading Places)…
I also want to throw in Pass the Ammo, starring Bill Paxton and Linda Kozlowski as a couple of rednecks, and Tim Curry and Annie Potts as a crooked televangelist and his loopy wife.
One more: Kuffs. People I’ve talked to who have seen it - almost no one, that is - either can’t STAND it, or think it’s hilarious. I am of the latter opinion. Stars Christian Slater, who actually manages to act occasionally.
Since one of my perennial choices has been named (Panic in Year Zero, about a family trying t survive Nuclear War circa 1960), I’ll name the others I usually give:
The Adventures of Mark Twain – Will Vinton’s underappreciated masterpiece. Wallace-andGrommit-style Claymation (Vinton invented the term. Copyrighted it, too, I think) excerpting the works of Twauin. James Whitmore does the voice of Twain.
The Last of Sheila – My all-time favorite mystery, beautifully oput together. Screenplay by Stephen Sondheim and Anthony Perkins (!)
Robinson Crusoe on Mars – far, far better than the dumb title suggests. I have to believe that they watched this when they were puttying together enemy Mine.
Creation of the Humanoids – offbeat, rarely seen science fiction flick. supposedly based on Jack Williamson’s “The Humanoids”, which it doesn’t resemble very closely.
The Lost Missile – One of Jerome Bxby’s 1950s SF flicks, and probably his least known.
Enemy from Space (AKA Quatermass 2) – A really different movie about
I forgot about that movie. I saw it once on a flight in the early 90s. It was quite funny but I barely remember it.
Well, no-one I know (except my dad) has ever seen it, or even heard of it. Must be a generational thing, I guess.