Yeah it's a bit difficult, I certainly wouldn't consider things that are thought provoking like Tarkovsky and challenge you emotionally as necessarily depressing
Obviously it's a very personal line with films that are really heavy when you can take 'em in and appriciate them even if they are superbly sad or depressing. Like two undeniably wonderful films from '11, We Need to Talk About Kevin and Shame, those were downers but they were still great films. Tarkovsky's films are mostly so emotional or sad that they're even more hard to endure, and they are also long.
However some films that have been amazing and at the same time have left me truly uneasy have been at least:
Dancer in the Dark-more of a musical I guess, tells a story of an ill eastern european single mother moving to America and hoping to make it there, but things don't really go as planned.
Gummo-Not a fan of Harmony Korine and his cheap attempts at shock value most of the time, however this one struck something.
Wisconsin Death Trip- A truth based film that covers random acts of murder, arson, insanity, suicide etc that happened on almost a weekly basis during the last decade of the 19th century in a small town of Black River Falls.
The Road-I think I've seen people mention it already in other threads.
Pan's Labyrinth-In the fascist Spain of 1944, the bookish young stepdaughter of a sadistic army officer escapes into an eerie but captivating fantasy world.
"During times of universal deceit, telling the truth becomes a revolutionary act."