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 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 likeable 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, VG Ai, Eden, or Gunslinger Girl (to use a more recent example) is not that they're 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.
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