Can I expand as to why this scene is my favorite out of all the movies?
Vader believed himself completely beyond saving.
"It is too late for me, my son."
He had been under the sway of the Dark Side for a good portion of his life. Perhaps a constant reminder of all that he had lost. Padme. His dreams to see the stars. His mother. Everything.
It’s as though he had given up completely.
Then, out of nowhere, this kid, whom he didn’t even know he had, even after chopping off his hand, and insists that he’s not such a shallow character… er, that he was once a friend, a force for good, and more.
Bitter and cynical, he thinks the boy’s delusional. He’s Darth Fricken Vader. The name alone inspired terror throughout the Empire and for good reason.
But then Endor happened. Luke had given himself up to save his friends, despite the fact that the Emperor already knew it was going to happen. Sneaky ol’ fart. And when he had lost to Luke, he thought he was done for after Luke cut off his hand. But Luke refused the Dark Side. And when the Emperor was about to kill his son, the same son that had spared him, Vader changed back to Anakin for that vital moment and had vanquished the Emperor, but at great cost to himself, because he couldn’t let the only person that believed him a better man perish.
Anakin knows he’s done terrible things. He’s made horrific mistakes that would keep anyone with a conscience up at night. However, just for that last moment, and whatever happens after he passes on, he is willing to accept what happens. And he dies as Anakin Skywalker, not Darth Vader.
This is what the story of Star Wars was about. Deeper than the Empire and the Rebellion, deeper than the Force. It was about Anakin’s redemption. It is one of the few rememption stories done well.
And despite all my issues with Lucas, I will consider this scene to be one of my favorites in cinema.