Luke, Leia, Chewbacca, and Lando risking their lives to rescue Han from Jabba the Hutt.
When Luke joins the rebel briefing (after realizing Leia is his sister), Leia immediately hugs him in front of everybody, notices he is looking at her intently, and asks "What is it?". Luke simply says "ask me again sometime."
The scene where he does tell her is one of the most touching scenes in the saga.
When Han and Chewbacca are reunited. Chewie even gives him a Bear Hug. He's just so elated to have his best buddy (and holder of his Life Debt) back. He even "pets" Han.
After Leia has been hit by blaster fire outside the shield generator bunker and Han is kneeling over her as troopers close in, she pulls out her blaster pistol and they reverse their CMofH from Empire.
Han: I love you.
Leia: I know.
The final lines between Luke and Vader/Anakin. Of course they border on Tear Jerker.
Anakin: Luke... help me take this mask off.
Luke: But you'll die.
Anakin: Nothing... can stop that now. Just for once... let me... look at you with my own eyes.
(Luke does just that, revealing the pale, emaciated face of Anakin Skywalker)
Anakin: Now... go, my son. Leave me.
Luke: No. You're coming with me. I'll not leave you here, I've got to save you.
Anakin: You already... have, Luke. You were right. You were right about me. Tell your sister... you were right.
Luke: Father... I won't leave you!
Anakin's smile the moment he lays his eyes on his son. It tells us his emotion with just one expression, he's proud of his children.
The line that "nothing can stop [his death] now" is doubly heartwarming when you remember that much of Anakin'sStart of Darkness in the prequels was caused by his inability to accept death as natural and inevitable, particularly the deaths of his loved ones. The scene can be read as Anakin both coming to terms with his past and encouraging his son not to make the same mistakes.
The Original theatrical ending. All of it. The highlight of the ending is when Luke joins the celebration and Leia runs up and hugs him. For some reason, the 1997 endings onward truncate and split up this scene. And of course, Luke seeing his father as the man he would have been had he not turned to the dark side, sharing a friendly look with Obi-Wan and then favoring his offspring with a loving smile.
It's kinda funny but, the newest version's ending is just as charming in it's own way. The young Anakin comes onto the scene in ghost form and gives everyone a rather shy smile. It's really very adorable.
The Special Edition ending has the entire galaxy celebrating when the second Death Star is destroyed, which means that the Imperial army is gone and freedom and democracy have returned. It's just... the fireworks, the cheering, the energy... *sniff*
Made even better when Luke sees his redeemed father's spirit, returned to the man he once was before he fell to the dark side, or as the man he would have been had he not turned, depending on your preference of editions, sharing a friendly look with his old master, and then favoring his son with a loving smile.
Luke and Darth Vader's interaction when Luke surrenders himself. Luke tries so hard to speak to his father and bring him back from the Dark Side, even though Vader repeatedly denies that there's any hope left for him. Heck, the fact that he calls him "Father" is an indicator that some love is there between them.
The fact that we see the first possible kernels of Obi-Wan and Yoda being wrong about Vader in this scene; Luke offers Vader to come with him, and for the first time across the entire trilogy, Vader's shell breaks and the Dark Lord of the Sith seems weary, quiet, and resigned. Doubles as a Tear Jerker if you consider that Vader is entirely aware of how his master operates at this point, and that Luke is his intended replacement.
The hug between Luke and Wedge, especially when you consider how Wedge and Rogue Squadron fought nonstop while Luke trained in the Force. Their relationship may have been mainly professional, but their embrace is warm and brotherly, each sharing their relief and thanking the other for their tenacity.
Threepio's "bedtime story" for the Ewoks. Highlighted by Leia snuggling close to Han, followed by an Ewok snuggling close to Han. Han's expression following the latter becomes a Crowning Moment of Funny.
And when Vader's killed the Emperor and is slumped against the railing, clearly dying by inches, Luke crawls over to him and supports him, doing his best to help.
One of the, possibly, more thoughtful tweaks to Return of the Jedi was showing various locations celebrating the fall of Emperor Palpatine. Yes, even Mos Eisley and the Imperial capital are celebrating his death.
Han was skeptical about Luke's plan to save him. But who can blame him? The first plan they did together, saving Leia aboard the Death Star, barely worked out, and the last time they were together, Han had to save him from Hoth's subarctic temperatures, that again, both barely survived. But after they get away, Han is grateful, telling him "Thanks for coming after me. Now, I owe you one."
When the heroes are about to be executed by Jabba:
It's blink-and-you-miss-it, but in the second movie, Vader says, "Only your hatred can destroy me." Think about it - there's a double meaning: it would kinda suck if your own son hated you, wouldn't it?
Luke's Shut Up, Hannibal! to The Emperor, but one line always stands out because of its multitude of heartwarming implications;
Luke: I am a Jedi, like my father before me.
Darth Vader's son, who has every reason to deny even the remotest connection with him, has just openly, and proudly acknowledged the relationship between them. Considering he's been trying to get his son on his side for two movies now, that's gotta mean something.
That the man he was, someone who has made so many terrible mistakes, is a person his son has decided is worthy of his respect and admiration. In fact, the implication of that statement is that he still considers his father a Jedi, and is therefore capable of redemption.
His son has utterly surpassed him; he's mastered himself and the ways of the Jedi, has gained power greater than his own without falling to the dark side, and has shown up alone to face the most powerful evil in the galaxy and has basically just won by refusing to give the Emperor what he wants- how proud would that make anyone feel, to see their son be so epically awesome?
This Alternate Character Interpretation: Darth Vader seemingly throwing away the fight just so Luke can win, Deep down he knows the Emperor expects only one of them to come out alive and isn't willing to kill his own child so in an act of attempted sacrifice he toys with Luke long enough to get him angry and leads both of them towards the shaft allowing Vader to put himself on the railing allowing Luke to deal him every blow till he cuts his arm off allowing Luke to come out as the victor.
Vader putting his hand out towards Luke as if it's a way to physically tell him to calm down and control his emotions
Han misinterpreting Leia when she says she loves Luke, and willing to step out of the way when Luke returns, not knowing Luke and Leia recently found out they're brother and sister. Even though it would break his heart to lose Leia, he loves them both so much that he'd be willing to part with his One True Love so she could be with one of his best friends. If that's not love, I don't know what is. Also counts as some serious Character Development from the Han at the beginning of A New Hope.