I have never actually cried at any anime (I'm a cold hearted weirdo). However, there have been times when I wanted io cry.

Death Parade is the closest winner to this category. One of the first things I saw about it was a skating scene. I didn't know what was going on at the time, yet when I saw it again within the show, it made so much more sense, and was very powerful.

Without spoilers, I won't say much more, but I'll give you a picture anyway.

Honourable Mentions:
Fullmetal Alchemist: The beginning of Fullmetal Alchemist (2003)

Death Parade: The entire first episode

Fullmetal Alchemist: Tucker's Chimera