There were a number of citations, some of which were shounen action manga with a sad plot development somewhere, some of which were various flavors of sad-ending shoujo romance, and some of which were actually pathetic in the model of Russian fiction. Here is my take:
I think the reason people's responses are all over the map here is that there's more than one kind of "sad" and different people respond to different things:
The commoner kind is the "unhappy plot development" variant. If you've read Video Girl Ai, you've seen the part where Ai gets taken back by her maker as defective. Not pretty stuff to read, since you already know Ai well, and you (if you've been reading this long) are quite attached to her as a character. Of course, since it's a happy-ending shonen romance, the situation is used as an opportunity for Yuta (the male lead) to grow a pair, as is often the case with these plots. Usually the mangaka will throw in something like this in a shonen manga with a romance sub/primary plot about 2/3 the way through the story arc. A slower (shoujo) example of the same thing is the stuff that goes on in Arima's head through the last third of Kare Kano.
A rarer, but recently more common sad setup is the "pathetic" variant. Pathetic, here, is used in the Greek drama sense, meaning "inspiring pathos in the reader." Even Ghost in the Shell has a little pathos about it, but if you really want to wade neck-deep into the pathetic, you can't beat material like Gunslinger Girl or Eden. Takahashi's Mermaid series (which I like best of all her work) is more upbeat, but still definitely pathetic in tone. To make a pathetic plot work, you have to set up likable characters in a continuing horrible situation. This is easy. The hard part is to be a good enough story teller that anybody actually wants to read it. One story I thought that bit off way too much but somehow managed to chew most of it was Kirara. It manages to be funny while still having a pathetic undertone...at least until the confused, hurried ending.
What keeps people coming back to stories like Crying Freeman, the Mermaid Saga, Video Girl Ai, Eden, or Gunslinger Girl (to use a more recent example) is not that the readers are gluttons for punishment, but that the author has done a good job of creating characters you like and situations you wish they weren't in.
Speaking of Gunslinger Girl specifically, I think it hits you a lot harder if you are somebody's parent. Likewise, I grew up around military working dogs, and recognize most of the conditioning and resultant behavior (accurately portrayed by the mangaka), which just makes it creepier.
Quote from corallein
Random thought: where would this put Grave of the Fireflies? I know a fair number of people that absolutely refuse to watch it because it's too sad.
Well, I'd file it in the same category as All Quiet on the Western Front by Remarque, and a goodly body of Russian fiction (like The Little Match Girl for a short and typical example).
Yes, it's really sad. That's pretty much its purpose as a movie. William Tecumseh Sherman said it best: "War is hell." Takahata designed the film to set up a pathetic and empathetic situation and used the framework to make a simple statement about war, its effect on civilian populations, and the consequences of putting pride and principles above pragmatism. I would argue that when Seita dies at the end of the film, it's a release from suffering and thus better than his alternatives at that point. It's very much like Russian fiction in that way.
Yes it's definitely pathetic. And what I've observed of different people's reactions to the film suggests that their opinion of the film is shaped almost entirely by their opinion of Seita and his actions. If the viewer empathizes strongly, he will be moved emotionally. If he regards Seita as a pompous callow youth, a less profound reaction results.
I think that one reason the movie is so generally effective is because Hollywood (and much of the Anime industry as well) have conditioned us to expect an 11th hour reprieve and happy ending. Movies (and books, and manga) that have the cojones necessary to deny us the happy ending are often better, but seldom big box-office hits. Consider the lawsuit over the ending of Blade Runner to be a good lesson in why really sad movies aren't often made. Ridley Scott finally got his happy/unhappy ending in Thelma and Louise, and I'd have to say it worked pretty well. Likewise, Ai-Ren isn't anybody's idea of a happy-cuddly story, but it nonetheless manages to say some profound (and hopeful) things about love and humanity even as both of the lead characters die. Sometimes you have to risk big to win big in literature, just as in other forms of gambling.
The great pity, of course, is that a movie by Isao Takahata (cofounder of Studio Ghibli and Hayao Miazaki's favorite producer) is only available at all in the USA at all because Central Park Media managed to get rights to it. Practically nobody in the USA outside of anime fandom has seen the movie. Pathetic, isn't it?