Films where there is no hope.

The Elephant Man - No explanation really necessary. Frederick Treves acts as a friend, but John Merrick still continues living a heartbreaking and tragic life.
Men Behind The Sun - One of the most emotionally distressing movies you'll ever see. There were moments that truly made me wince watching them, one being so bad that I started yelling angrily at the screen in total despair. A lot of is required to stomach sitting through the entire thing.
No Country For Old Men - As long as Anton Chigurh goes around causing terror in the town, nobody will ever feel safe and may be snatched away at any time.
Leaving Las Vegas - Nicolas Cage and Elisabeth Shue's inevitably hopeless love story will rip your heart out.
A Serbian Film - Every time you think you've seen the worst, it somehow manages to top itself.
Boys Don't Cry - Knowing what happened in real life, it's downright impossible not to feel the impending sense of doom even when Brandon is at his happiest.
Precious - There is a little bit of hope, but you can never escape the feeling that it's fleeting. Mary seems unable to escape her nightmarish home life, and Precious sure as hell is anything but. Both characters are coated with tragedy, but one tries to be a good person despite the abuse while the other passes the cycle down on her own daughter instead.

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The Gray

The Road for sure. I've seen lots of grim movies but that one had enough believability to leave me wanting to follow up with something brainless like an old Jerry Lewis movie.

Little Orphan Annie - You think the misery of the orphan will end, but there's always another musical number waiting in the wings.

Human Condition trilogy is soul-crushing with no realistic expectation other than dank demise.
Ran has no hope. Nothing good happens to anyone in this film, and yet I love watching it.
Schindler's List has no hope in the context of the film. As viewers we know the Allies were coming, but the people in the film had no reason to believe that.
The farmers in Seven Samurai have hope but the samurai have exactly none. They knew that they were there to fight and that they were not there to survive.
Kenneth Branagh's Frankenstein is bleak as anything. Mr Frankenstein loses people left and right and he slowly deteriorates.

I need to stop now. This is getting depressing. (I love depressing films) (but I have depression issues) (so I have to be careful).

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Thanks again, Mr Portridge.

I totally forgot about that one. That is a good pick, my friend. Anton gets battered and bruised, but is never stopped, at least in the context of the film. It definitely fits the bill.

I just thought of another one. Parasite has no hope. The families crumble into death and destruction and no one comes out ahead.