Three people answered, making a total of seven different guesses, all of which were wrong (well, I might give partial credit for one of them...).
The answers are: The arrival of the Black Pearl at the Farthest Shore; Elizabeth's "Hoist the colors!" speech, and the re-appearance of the Flying Dutchman with her new captain, just before the battle with the Endeavour.
Explanations, of a sort: I don't cry because I am sad, or in pain. Ever. I cry because I am happy, sort of. I would say that I cry out of joy, but that just begs the question of defining joy. Dementia says that I cry at triumph over adversity, which makes a certain amount of sense.
My best explanation, with regard to fiction, is that I cry at moments when there is a reconciliation between the expectations of the characters and the expectations of the story. Within the story, things are bad and getting worse; outside the story, it is clear that things MUST change-- and they do. Barbossa leads his crew to the Farthest Shore, and now they are trapped in the netherworld with no ship, and no sign of Jack-- and then the Pearl appears over the dune with Jack perched on the foretop yard. Magic.