Kemono no Sou-ja Erin
Kobato - this one has some romance in it, albeit highly innocent stuff
Tokyo Magnitude 8.0
Kowarekake no Orgel OVA (It would be so wrong if I did not mention this one since my user name is of the main character!
)
All of them were very moving.
For me I would also add the Aria trilogy. It is more of a "being deeply touched by something beautiful" bringing forth of tears as opposed to "being moved by sadness".