Cried three times during Fruits Basket--the episode with Hatori's backstory, the episode with Momiji's family, and the last bits with Kyou.
Cried twice during Trigun, during the flashback episode with Vash, Knives, and Rem, and with Wolfwood (and, for the record, actually flinched and whimpered when Zazie got shot, but that doesn't count).
Cried during the final episode of Cowboy Bebop. Luckily, dad had recorded it, 'cause we had to pause the tape due to my sobbing.
Cried during Wolf's Rain, and multiple times during Fullmetal Alchemist.
When I was little, the episode of Po