Anything from Terry Gilliam really fits as a cult movie, because his work is so polarizing. Never doing gangbusters at the box office but always finding enough of an audience to become classics, Terry's work is often found in a movie library. It's easy to say this is a film about a man wrestling with the commercialization and bureaucracy of his world in contrast with his desire to be free, but the film borders on being as indecipherable as a drug trip so words fail me in describing the plot. Suffice to say, it's debatable what happens in many parts and that's what makes it so sad.
Despite it being established that once Elizabeth Swann's dad was captured and tortured, everything that occurs afterwards was only in his mind, there are still many who reject that and insist that he escaped. Do you know why? Because the thought of the bad guys winning so entirely and thoroughly is so unpalatable that many only watch the cut where it's not revealed as a dream. It's so sad that people close their eyes and ignore certain scenes to make it better. How's that for sad?
3. Donnie Darko
Much like Primer, this is a film that may make sense to you when you see it, but afterwards you'll find yourself reading plot summaries online just to realize you had no idea what just happened. There's so much not explained in the film that the director just assumes we understand, like pocket universes and people destined to correct the time flow before the pocket universe collapse on itself. It's super-cult, but still a worthwhile film.
My knee-jerk reaction is just listening to the "Mad World" song as the reason why this film is sad. Not sure that counts, so I'll list another. Donnie is portrayed as a very goth kid with not the best social skills, however he bonds with a girl through the film and seems happy. Then she's killed for (insert plot here) and we really feel the weight of his loss. Not having a vast network of relationships, this one human connection meant the world to him, and its loss is huge. When the pocket universe rejoins the normal time stream (this movie is dumb) and everyone is brought back to life, we have a scant few moments to hope Donnie will gain happiness...then he's crushed by a jet engine. You kinda have to be there.