1. Spock's death and subsequent funeral. Nothing else even touches this.
2. David's death. More specifically, Kirk's reaction to David's death. William Shatner's finest moment as an actor.
3. The death of the Enterprise. No list of moving Trek movie moments would be complete without this.
4. The score for the TWOK end credits/TSFS opening credits. There's an awful lot of emotion in that music. Kudos, James Horner.
5. Enterprise-A flying off into the sunset, so to speak, followed by the main cast's signatures. Truly the end of an era, certain characters' appearances in Star Trek: Generations
6. Geordi seeing a sunset with his own eyes for the first time.
7. The "rebirth" of the Enterprise with the reveal of the Enterprise-A. "My friends, we've come home."