This is actually almost embarrassing, but the first movie I remember having an emotional breakdown occur (outside of Old Yeller, of course) was in Silent Running when the one robot was sacrificed (I forget the reason). In retrospect I was a bit ill at the time, they diagnosed me a few days later with gastroenteritis, and IIRC walking pneumonia. It was a sad few days for me (oh, and I was like maybe 10 or 12).
Jack