I had to think for a good several minutes and even searched my externals to see what I had to see if I could add anything new to this discussion.
Haven't seen
Grave of the Fireflies. I'm scared to, really. I've built up the expectation that this thing is the saddest thing ever animated, and if it doesn't live up, I'll be horribly disappointed and trash talk this for life, which I don't want to do.
Did see Saikano. THAT was depressing. Just a feeling of utter hopelessness at the end, and the atmosphere throughout the anime was depressing in itself.
I must be one of the few who did not think Clannad was all that sad. It had to be because I played the game beforehand, and knew what was coming.
For me however, the most depressing anime was
ef - a tale of melodies. Yes, the second season was inferior to the first in many ways. For me at least. Yuuko/Himura and Mizuki/Kuze just weren't as entertaining as Hiro/Miyako and Renji/Chihiro. But Yuuko's story is so unbelievably depressing that I couldn't even cry about it. It was more shocking than sad, and all the more depressing because of it. I define 'depressing' to mean a state of mind where you are not happy, cannot be made to be happy, and there is no end in sight. You have to really think of what she went through as a child to fully get the impact.
Her offer to be Himura's younger sister was denied by Himura. She was taken in by someone else, who raped her on Christmas. She wasn't of age. Far from it. She tries to break free of her past, slowly but surely beginning to succeed, finding love and happiness at last...and is randomly killed in a car accident.
She did nothing to warrant such a life. Utterly depressing.