There have been a few scenes that make me tear up, several of which have been mentioned; the final scenes of the final episode of both TNG and DS9, the final scenes in "Duet" (Kira and Marritza's last conversation in the cell, as well as the very end of the episode), and the final scenes with the Doc and his family in "Real Life", all come to mind as being among the most prominent such moments for me.
Another one that I really like is in DS9's "Accession". Kira, feeling she must follow her d'jarra, resigns as XO, and comments that Sisko shouldn't have trouble replacing her. To which he replies: "I don't doubt that I can find someone to fill your post. But to replace
you?" His tone of voice and the look in both of their eyes make it a touching scene that really shows how much they have come to respect one another, despite - or perhaps in part because
of - the unique difficulties they've had to overcome in order to function well as a team.
However, topping them all is Picard addressing the crew to inform them of Sito's death at the end of "Lower Decks", with the reactions of her friends, and then the Ten-Forward scene that follows. That whole sequence is masterfully done and really gets me like nothing else in Trek does (and the episode itself is one of the best in the entire franchise).