Much like truly terrifying moments, I love searching for truly sad and emotional moments. A few that come to mind:
Ninth to Eleventh Doctor Who have some really devastating scenes, as do every single one of the special episodes. Nothing really compares.
Elfen Lied was terribly, terribly sad. But sadness doesn't have to be a negative emotion.
Likewise with Full Metal Alchemist, which balanced it out skillfully with other moments that increase the contrast of the tragedies.
A Time Traveler's Wife was pretty damn heartbreaking. Hiddleston is pretty unique in that the sadness he's portraying truly seems to be his. He has a moment like this in War Horse as well.