I agree, I just watched Elfen Lied and it depressed the hell out of me.
Spoiler (highlight to view)
I mean, they spend the whole series (I'm talking about the anime here, I haven't read the manga) having you build a rapport with Lucy/Nyuu and then they sort of make her an irredeemable character. Even though from the very beginning it's shown that she is fully capable of murder, nobody really cares about all those no-name guards she rips apart in the first episode (the clumsy secretary being the exception to this, but even still, it's hard to really be sad when a character you haven't even been introduced to is killed). She rather sadistically rips the arms and legs off of Nana, but even this can be forgiven on the "no harm, no foul" principle (considering that she does get replacement limbs that seem to work just fine). But when it's revealed that she killed Kouta's sister and father you kind of stop rooting for her to become a good and complete person and start hating her. Kouta was her only true friend and she killed his family out of. I guess. revenge. The abuses that she herself suffered make you pity her but the choices she made were so extreme and terrible that you have a hard time forgiving her. She apologizes in the end and you do feel like she's truly sorry but her actions are unforgivable. Couple that with the fact the ending leaves you with a feeling of incompleteness and it's very depressing indeed.