Clannad
Air
Kanon
Chrono Crusade
Gundam wing can be?
Gundam Zeta
Gundam Unicorn
stuff
I think Full Metal Alchemist is one of the most depressing ones I have seen. Sure, it has comedic relief but it sheds light on real world issues that won't ever be solved due to human nature. Also, Nina...
edit:
Welcome to the NHK was pretty sad for me as well. It was painful to watch, not that it's a bad anime, the story telling and animation was great. It's just hard seeing people in those kinds of situations.
Zeta can be depressing but I've seen it over and over so the more I watch it the more I tend to get a bit more indepth with characters. Same with wing. But for unicorn, the novel goes more in depth than the actual show so I don't want to talk to much of that.
It really depends on the viewer to find something sad and not everyone has the same tastes. I love heero yuy for example and found a lot of story inside that outer rock hard shell of a silent protagonist and someone else who watches it might find him just bland as hell. Though its all fine to have disagreements
War in the pocket and ms team wing and zeta and unicorn I love everything.
Ano Hi Mita Hana No Namae O Bokutachi Wa Mada Shiranai is also a bit depressing too. It's also pretty short.[Image: http://media.tumblr.com/tumblr_m9gcvqToXY1qzckow.gif]
Corpse Party: Tortured Souls hit me right in the feels.