I've never actually cried watching an anime but with this one I was pretty close. The anime that caught me off guard is Paracyte
When I first started Paracyte I expected to see some horror/action and that was all. I was so wrong I was almost brought to tears when Shinichi's mother died and a Paracyte took her place and when Reiko shielded her child from the police shooting at her and Shinichi saw the face of his mother...... I was really close to crying.