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Tear Jerker: Avatar
The destruction of Hometree. and Neytiri's father's death.
Especially tearjerking for the hundreds of Na'vi breaking down crying.
Selfridge finally realizing that he made a mistake while watching the destruction of Hometree. But it's too late.
Also when Trudy's gunship was shot down.
When Jake is formally adopted into the Omaticaya, we see Grace looking on, doing her damndest not to cry.
Tsu'tey's death, especially in the extended cut. "He was my last shadow."
Also, in the Extended Cut, The Na'vi school. We first see it being used as storage after being abandoned, and after Jake sees some bullet holes in a blackboard and asks Grace, she snappily changes the subject. Later on, after Jake and Grace have grown closer, she tells him exactly what happened. Sylwanin (Neytiri's sister) and a group of young hunters attacked an RDA bulldozer and ran to the school. When the troopers arrived, they not only killed Sylwanin right in front of Neytiri, but also many of the students. Grace's "I got most of the children out" line really drives it home.
The opening shot
Neytiri holding human Jake when she saved him from suffocating.