Luke hearing Obi-Wan's voice during the Trench Run. There is a wonderful realization that Luke is not alone, even with Darth Vader on his tail, and the old Jedi Knight is still around in spirit to help.
Kenobi:Remember, the Force will be with you, always.
After C-3PO spends the whole movie berating R2 and saying the whole situation is his fault, before the attack on the Death Star he just tells R2 to come back safely. "You wouldn't want my life to get boring, would you?". And when he sees R2 has been damaged, he tells Luke "Sir, if any of my circuits or gears will help, I'll gladly donate them!"
The medal awards ceremony, in particular the gentle violin melody celebrating peace and hope that follows the thunderous martial anthem of "The Force Theme."
Vader actually seems to have a fairly good rapport with most of his subordinates in this one (with the obvious exception of Motti). Daine Jir feels free to question him to his face and Vader listens, he and his wingmen clearly work well together (even if the one guy messed up, he still tried to protect Vader from the Millennium Falcon), and in a deleted scene, Chief Bast is comfortable complaining to him about Tarkin's actions, which he considers a foolish waste of time.
Obi-Wan consoling Luke after discovering Owen and Beru were murdered by Stormtroopers while he was away.
Obi-Wan: There's nothing you could've done had you been there. You would have been killed too, and the droids would now be in the hands of the Empire.
The scene right after Obi-Wan saves Luke and the droids from the Tusken Raiders. Luke and Kenobi find C-3P0 with a severed arm and the droid suggests he be abandoned while the others get away. Luke's reaction is simply that of course they are not going leave their companion behind. If that does not mark Luke as a hero you can respect, nothing will in the series.
And when Threepio is lamenting about how there's no point in the others being put at risk to save him and how he's done for, Luke comfortingly replies with "No you're not, what kind of talk is that?" He's actually treating this droid — who many others could have dismissed as just a machine and abandoned to get out of danger — like a person, and it really shows what a good person Luke is.
Although, in a bit of Fridge Logic, at that point in the movie, Luke is still focused on retrieving a newly-purchased, and probably expensive, droid so he can get to work on his farm chores, and his search has resulted in the other new droid becoming damaged. He's trying to preserve a valuable piece of equipment, and if that means he has to cajole and encourage Threepio to get him moving, then so be it.
A meta-example, overlapping with awesome; at the 1997 MTV Movie Awards, Chewbacca was given the Lifetime Achievement Award - in the form of the medal that he never got at the end of Episode IV. The really awesome part? George Lucas allowed it on one condition...that Peter Mayhew himself wear the wookie suit. Even better, Carrie Fisher was the one who gave Chewie his medal. The ovation of the crowd was deafening.
Han spends the film belittling the Jedi and the Force, however, he says "May the Force be with you." to Luke before the Battle of Yavin.
At first Han doesn't get along with Luke or Leia. After their adventure on the Death Star they're best friends.
Leia draping a blanket over Luke and comforting him after Obi-Wan's death.
The first time Obi-Wan takes off his hood and sees R2-D2. Yeah, it's a big fat retcon, but it's easy to interpret him being coy with his phrase "I don't seem to remember owning a droid." With R2's little beep in response, you get the feeling the two of them are in on the secret while Luke and Threepio aren't.
An actually good use of From a Certain Point of View, since any droids Obi-Wan did work with during the prequels would have been the property of the Jedi Order itself (likely as an extension of the Republic government), and Artoo in particular was owned by Padme/the Naboo government/Anakin. So technically, Obi-Wan never did own a droid, especially not Artoo.
Meta example, but Mark Hamill recalls goofing around on set to make George Lucas laugh because the director looked like he was about to cry. It's nice to see actors willing to mess up just to make their directors crack.
Watching the battle of Yavin 4 after witnessing the events of Rogue One. The Death Star DOES get destroyed, Galen Erso's calculated design flaw WAS exploited, Rogue One's sacrifice was NOT in vain.