There are simply too many emotional scenes or moments to list in a single post. But here are some that always make me shed at least several single man tears...
"THE VISITOR" - I am a total mess after this. Every. Single. Time. One of those episodes that absolutely transcends the genre and speaks to everyone.
"The Offspring" - Lal's final scene, thanking Data for her life... that just hits hard. And then Data walking onto the bridge, saying he transferred her memories into him because she so enriched his life that he couldn't allow her to fade into oblivion... a father just lost his daughter, but he finds a way to keep her spirit alive.
"HARD TIME" - after O'Brien almost kills himself, he enters his quarters and Molly just runs to him and says, "Daddy's home!", and hugs him. That just gets me every time.
"The Inner Light" - the ending, with Picard clutching the flute and then playing the song.
STAR TREK II: THE WRATH OF KHAN - Spock's death scene. Kirk speaking at the funeral. And as I've gotten older... when McCoy says, "He's not really dead. As long as we remember him."
"Et in Arcadia Ego, Part II" - Picard and Data's final scene.