I'll add a few more films since this thread is still alive. However all of them are little known American indie films that "nobody" watches, but I thought were unfairly maligned and/or critically dismissed:
The Hawk Is Dying. 2005 film. Character study on monomania and existential regret, as seen through the eyes of George Gattling, a rumpled and obsessive Paul Giamatti obsessed with falconry, except that he kills all the hawks he tries to train.
Claire Dolan. Lodge Kerrigan's 1998 follow-up to his breakout Sundance indie flick
Clean, Shaven. He became a critical darling with his debut's searing portrayal of schizophrenia through the eyes of one man trying to re-unite with his daughter; his second film deals with a New York call girl (Katrin Cartlidge, icily brililant) trying to navigate an emotionally barren and taxing existence with a hostile and controlling pimp on her back (Colm Meaney, who most know as Chief O'Brien of Star Trek fame). Lodge Kerrigan didn't get the same accolades this time 'round, though populist critic-of-the-masses Roger Ebert gave this art-film four stars.
Sorry, Haters, 2006 psychological drama about a severely emotionally damaged woman who works as a low-level executive at an MTV-esque entertainment channel, who hijacks a Syrian cabbie one night in a twisted psychological game of manipulation. Really stunning character study in repressed rage, envy, and the curdled milk of the American Dream, but told through the perspective of a native and a hard-working immigrant. By far Robin Wright's best role of her career (most know her as "Princess Buttercup"). Guess critics found this movie too corrosive, however.
On a lessor note, I'll add
The Black Dahlia to the list. It's not an independent film, but a big-budget Brian De Palma noir period film. It's was critically panned, and rightfully so. It's comically misguided in its hard-boiled script, casting choices, hammy direction, and methodology of building tension. However, it's so colossally un-self-aware of how over-the-top it is (all the drama is played "straight") that it's destined to fall into a "so bad it's good" category in the midnight movie vein. I don't think I've laughed harder at a non-comedy film.