Star Trek: First Contact/Heartwarming

"Lily: I envy you; the world you're going to.
 * The epilogue, where aliens land to find the human who flew Earth's first warp-drive vessel. When the visitors reveal themselves to be, you know it is the Dawn of an Era where humanity's time of desolation and despair has ended and its hopeful beginning of the building of The Federation has begun.
 * Every little moment of wonder from the 21 century Terrans led to a slight dampness of eye, because it's so perfectly what Trek is about--this is what the future could be! And then when Definitely something in the eye.
 * Enterprise later used this to illustrate how the Mirror Universe diverges, with Cochrane, and it works very effectively as a deliberate Shocking Swerve because of how heartwarming the original scene was.
 * A more subtle part is the Enterprise crew being unable to resist the urge to observe the moment for themselves. They ought to have just beamed back to the ship... (And Sisko shouldn't have introduced himself to Kirk, etc.)
 * Picard and Lily's final scene together, as this all unfolds.

Picard: I envy you; taking these first steps into a final frontier."

""I owe him the same.""
 * Picard going back for Data as the ship is evacuating because he's certain the android is still alive. He justifies it by recalling how the crew risked everything to save him from the Borg years earlier.

"Picard: I apologize for some of the things I said to you earlier.
 * Cochrane's subdued "Oh, wow" at seeing the Earth from space.
 * Picard apologizing for calling Worf a coward:

Worf: Some?

Picard: As a matter of fact, I think you're the bravest man I've ever met."

"Riker: "Don't try to be a great man. Just be a man, and let history make its own judgment."
 * Riker helps Cochrane get over his fear of destiny:

Cochrane: That's rhetorical nonsense. ... Who said that?

Riker: (grinning) You did, ten years from now."

"Data: I believe I speak for everyone here, sir, when I say, "To hell with our orders.""
 * Picard telling Riker to "stay out of history's way" when evacuating the Enterprise crew to Gravett Island. There's something charming and heartwarming about the scene - probably because they think they won't be able to return home and it's sort of a retirement package to live out their days on a deserted Polynesian island... Wait a minute...
 * After hearing how badly the fight is going for the Starfleet forces, Picard announces his intention to violate orders and take the ship into combat to help, but will allow any dissenters to speak up. As funny and awesome as it is, Data's response after the beat is also a heartwarming display of loyalty: