During the battle on Hoth, Luke single-handedly takes down an Imperial Walker, by himself. At that, you'll understand why the Emperor is so concerned about the kid; as in, "If the boy can do that with barely a few days instruction from Obi-Wan Kenobi, what could he do once he is properly trained?"
And of course the Walkers themselves.
During the same battle, the Rebels manage to disable a Star Destroyer with the Ion Cannons, creating a gap in the Imperial blockade for the Rebel ships to escape through.
Little Yoda lifts big X-Wing.
Luke: I don't believe it.
Yoda: That... is why you fail.
Luke Skywalker VS Darth Vader.
Above all, when Luke is clinging to that ledge, thoroughly beaten by Vader both physically and emotionally. Luke willingly defies Vader's offer - "Come with me, it is the only way." - and steps off the ledge. Not even knowing if he would survive the fall (he does, barely).
For Vader, when he starts picking up random pieces of machinery and tossing them at Luke in the middle of the fight. That's when you really understand that, yeah, Luke's pretty handy with a lightsaber, but he iswayout of his league here.
Compounded by the realization that Vader isn't even trying to kill Luke. He wants him alive but beaten to within an inch of his life, so as to be vulnerable to his suggestion to join forces. Imagine how brief it would have been if Vader had just wanted Luke dead.
Further emphasized that while Luke adopts the standard two-handed grip on his lightsaber at the start of the match, Vader opens with a more casual one-handed grip and bats away Luke's initial attacks with what is clearly contemptuous ease. Those first few strikes serve as the first inkling that Luke may have just bit off a lot more than he can chew.
The fact that, despite the handicap Luke faced, he actually managed to land a blow on Vader's shoulder, though the armor stopped it.
The setting for this particular duel was also amazing. The eerie, low-lighting of the carbonite chamber, the fog from the machines, and Vader's breathing grimly cutting in through the silence. A truly masterful set-up to the fight.
Also, when Vader kills Admiral Ozzel. Ozzel isn't even in the same room, and yet he easily force chokes him; distance is no object to Vader.note Although more to the point, distance is no object to the power of The Force.
When the Millenium Falcon's hyperdrive finally works thanks to R2.
Wedge and Wes being the only Rebels to actually take down an AT-AT with their tow cables.
Boba Fett doesn't even flinch when Darth Vader gets in his face about the disintegrations.
How about the fact that Boba is able to get semi-huffy with the Sith Lord and live!
Han Solo after being tortured. When he finds out that this was all to lure Luke into a trap, he uses a bit of strength he has left to punch Lando before being restrained. Lando was in the middle of a Heel-Face Turn at the time, but the fact that Han's best friend putting his other best friend in danger being the last straw for him was pretty awesome.
As Han Solo is lowered into the carbonite freezing chamber, Leia declares her love to him. She doesn't get the response she was hoping for.
Leia: I love you!
Han: I know.
The big reveal, in some of James Earl Jones's best vocal work.
Vader: No. I am your father.
Jedi deflecting blaster fire with their swords is neat, but Vader doesn't even need to show off - he just raises an arm and deflects/absorbs the blasts with his palm!
John Williams' music is its usual awesomeness, but two aspects of this score particularly stand out. Firstly, the Imperial March; rarely has music been quite so badass. The second is at the very end of the film: The Rebel fleet has fled the galaxy after the destruction of their main base, Luke is psychologically shaken by the confrontation with Vader and learning the man is his father (not to mention getting his hand lopped off) and Han has been frozen in a block of carbonite and taken off by a notorious bounty hunter to be sold to wicked gangster. But as Lando speeds off to rescue his friend and Luke and Leia stare out at the stars, what music is blaring behind them all? Han and Leia's Love Theme.