"Chinatown" has one of the best classic downer endings. The woman Jake is trying to keep from getting hurt, gets hurt and all anyone can say is "Forget it Jake. It's Chinatown."
"In The Mood For Love" By Wong Kar Wai. More bittersweet than a downer, but still, the sadness and regret of never being able to be with someone you love because of societal norms is rather sad.
"Songs From the Second Floor" by Roy Andersson. The closest thing to a main character in the film bemoans how he is being persecuted by the ghosts of all the people he took advantage of. Like many people, he is completely unaware that he is actually the bad guy in the story.
"Dr Strangelove" While immediate disaster is averted, the film ends with the implication that it's only a matter of time before we all blow ourselves to bits.
"Oldboy" An enigmatic ending. Things definitely didn't work out as planned.
"Another Year" by Mike Leigh.
"Naked" by Mike Leigh
"Miller's Crossing" by the Coen Brothers. Tom Regan cannot keep following the foolish decisions of his one true friend and ultimately must part ways.
"Do The Right Thing" by Spike Lee. Nobody does the right thing.
"Dog Day Afternoon" By Sydney Lumet. Things go from bad to worse and then it goes downhill from there.
"A Serious Man" Again, an enigmatic ending, but it's not looking good.
"Fat Girl" You can tell she ain't gonna have a happy life.
"Unforgiven" Even the heroes turn out to be bad guys.
"Monster" Nobody comes out okay in this one.
"Seven" Pretty much the mother of all downer endings.
"Taxi Driver" More disturbing than a downer, but when you think about it, you know something real bad is going to happen after the film ends.
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Never let the weeds get higher than the garden,
Always keep a sapphire in your mind.
(Tom Waits "Get Behind the Mule")