I know this is a total hijack, but for the record, he was in their vaudeville act for a few years. He was replaced by Zeppo, who appeared in the first few movies, then retired.
Back to the subject at hand - I can’t think of anything new to add, but I heartily second In the Company of Men (warning, not a date movie), Dancer in the Dark, and Audition. The Grey Zone is pretty bleak, too, if you can get past the accents.
In the vein of Requiem (i.e. dark, depressing, claustrophobic) Martin Scorsese’s Bringing Out The Dead comes to mind. Took me a couple tries to get thru the whole thing. Great film though.
You suck, I was all proud of myself for getting ready to recommend Buffalo '66, thinking how original and well-versed I would appear. Then here you are not only stealing my thunder, but you up the ante and also list Kalifornia, which I hadn’t thought of, despite it being in my DVD collection. Needless to say, I second both.
Things to do in Denver when you’re Dead is a straightforward mob movie, not even as jarring as the Sopranos season 1. But Gabrielle Anwar is yummy-nummy, so that alone is worth the rental. And Christopher Walken’s scenes are pure gold. (As is pretty standard for him.) In the same vein, check out True Romance…the pure-gold Christopher Walken-Dennis Hopper scene is a classic. But now I’ve got to add Reservoir Dogs, and maybe even Killing Zoe, so let me just stop and say check out anything written by Tarentino or Roger Avary. (Stop me before I mention The Rules of Attraction.)
Wild At Heart is okay.
But to move further into the realm of disturbing, Closet Land is a personal favorite. I love “stage” movies…few characters in a single room. This one has only one set and two actors: Madeleine Stowe and Alan Rickman. So good…so good. Staying in the same genre, which I won’t reveal, also check out Death and the Maiden.
Btw, Highway also stars Jared Leto, to tie it in with Requiem for a Dream. And here is het male #2 checking in to say I would have easily gotten a chubby from Jenny’s stag party show if it hadn’t been interwoven with mom’s electroshock. Amputation and regurgitation are one thing, but a helpless old woman getting her brains fried…that just made me ill.
But speaking of Highway reminds me of Freeway, which contains my favorite roles of both Reese Witherspoon and Keifer Sutherland. I know, they don’t sound like actors you want to see, but they outdo themselves in that movie.
Henry, Portrait of a Serial Killer kinda made me wanna go randomly kill people. But I’m still unsure if I liked it or not.
Don’t forget the classics: A Clockwork Orange and Brazil.
Leaving Las Vegas is disturbing in a depressing sort of way.
Shallow Grave is loads of fun. I finally saw it recently; not bad at all.
For old school camp, try Liztomania and/or Lair of the White Worm.
I know I’m forgetting a bunch, but my original idea of a quick list has gotten out of control, so I’ll end with another vote for Trainspotting, which also reminds me of Lock, Stock & Two Smoking Barrels.
I had originally recommended (and then snipped for lack of disturbing) Run Lola Run, but upon re-reading the OP, I have to say you should check it out if you haven’t seen it. If you like Run Lola Run, also check out Cherish. It’s damn near an homage toward the end.
I forgot to second American History X, which reminds me of Citizen X, which was (like Freeway) an HBO original back when they made kick-ass original movies.
Se7en goes without saying, doesn’t it? Brad Pitt made several great ones.
I’m sure I’ll think of more.
Which reminds me: I still cannot believe Maggie Gyllenhal agreed to do Secretary. It’s a romantic comedy for the alternative crowd. But now I’m veering into territory that would include Crash. Holly Hunter was clearly on drugs when she agreed to that movie.
The title Angel Baby reminds me of Angel Heart, though I can’t seem to recall if the title is one word or two.
Now, a film which is not disturbing for disturbing’s sake. A really intense portrait of an existentialist vagabond: watch Naked by Mike Leigh.
Top-notch character development, acting (by Thewlis and the whole crowd), and even cinematography.
If it has already been recommended, I missed it and I apologize in advance.
The 25th Hour
I thought the two, although they have different styles of presentation, shared several of the same themes. It’s not upbeat, and not happy, but it’s a great film. It’s about dealing with what life gives you and accepting it and yourself, failures and all. It’s worth it just for Cusack’s five-minute rant in the mirror.
Most of my favorite disturbing movies have been mentioned but I’ll add;
Ichi The Killer (Japanese) - Extremely black humor, stunningly violent and very gory
Bad Lieutenent - Very depressing study of immorality
The Cook, The Thief, His Wife and her Lover - Very dark jacobean comedy
Kids/Bully - Not your average teenagers (or maybe they are?)
Leaving Las Vegas - Very distrubing view of what happens you hit rock bottom
Battle Royale (Japanese) - Teenagers forced by the government to play “The Most Dangerous Game”
Suicide Circle (Japanese) - Teenagers randomly commit group suicide
Irreversible Very well acted and directed story of rape and revenge.
Told backwards like Memento. I found it very very intense and shocking.
I cannot warn you enough of how shocking two scenes are in this movie. Most realistic rape scene ever filmed IMO and the most graphically insane violent scene.
If you can handle it it’s well worth the look but seriously BE WARNED. The movie messed my sister up for about 2 weeks, nightmares etc.
Well, you must be one sensitive guy. And all your friends must be very sensitive too. How nice for all of you. raises eyebrow
How could we neglect to mention Pink Floyd’s The Wall for disturbing?
Oh, whine, whine, whine! You got to mention Leaving Las Vegas, Brazil, and A Clockwork Orange, so stop your complaining. 
By the way, I’ll see your Lock, Stock, And Two Smoking Barrels and raise you Snatch. Brick Top…:shudder:
These aren’t really like Requiem but i’m sure you will dig them the most anyway as they are thoroughly brilliant: La Haine and City of God. Also Irreversible but I thought this film was pointlessley graphic and wasn’t actually as good as everyone seems to think it is. On another French film tip check out The Piano teacher for weird SM repressed teacher action complete with genital mutilation and spunky tissue sniffing.
I have to add one to my list - À la folie… pas du tout (He Loves Me… He Loves Me Not). It doesn’t seem at all intense in the beginning, but when the perspective shifts, you see things much more clearly.