I have cried at many anime. Probably every anime I have has made me cry. It's not really the story (usually) but just moments.
A lot of the ones not mentioned here were...
Welcome to the NHK? No cries...?
Haibane Renmei is also sad.
I found Yumekui Merry to be very emotional, but I think certain color schemes make me more open. That's why VNs can be very sad, because they can have very light schemes like 'if my heart had wings.'