Hell no. Sure, there's some bits that I could empathise with and some bits where i went "Aww, shucks. That kinda blows for you." However, it's not a particularly sad series.
I'll have to second/third/whatever the Grave of the Fireflies people.
Also, I find Cowboy Bebop to also be in its own state of melancholy. It's hard to describe, y'know? *found Faye obnoxious but enjoyed her backstory*