The opening sequence to Up gets me every time. I've never seen such an effective combination of music and animation to convey the emotion of the various moments in that sequence, and all without any voice acting at all.
I was also shown two movies in school about the aftermath of nuclear war. When the Wind Blows is beautiful, touching and sad.. and made me, and many others in my class, cry.
The other was called Threads, which frankly made is cry in distress.