After the opening crawl, a single Republic attack cruiser rolls across the screen, to the sound of lone drumbeats. Two Jedi Starfighters race over it to the most bombastic and cheer-inducing take on the Force theme ever: we know exactly who's piloting those starfighters, what they're about to do, and in the space of a single scene, that this is the movie we'd been waiting twenty years for.
To quote the novelization: "Though this is the end of the age of heroes, it has saved its best for last."
Anakin really gets to show off his Ace Pilot skills. He tricks two high-precision homing missiles on his tail into hitting each other, pilots his interceptor so finely that he crushes a buzz droid between his and Obi-Wan's fighters without damaging either ship, and blasts the Invisible Hand's hangar shield generator right as he's charging in.
And while skidding across the hangar deck, Obi-Wan leaps out of his starfighter to cut several battle droids with his lightsaber.
Anakin utterly destroys Count Dooku in what quickly becomes single combat, and carries an unconscious Obi-Wan on his back like a rag doll.
Grievous escapes a confrontation with Anakin and Obi-Wan by shattering the control room's window and exposing the entire room to the vacuum of space. As smug as he may be, that takes balls - or in his case, lack thereof.
And then Anakin manages to crash-land the wreckage of the Invisible Hand on a Coruscant runway. To reiterate: he landed a 3570-foot long dreadnought that was never designed for safe landing!
Palpatine's meeting with Anakin at the opera house is as creepy as it is awesome. The music already sets the intensity of the scene, but Ian McDiarmid's acting adds to it with the "Tragedy of Darth Plagueis the Wise". Perfect storytelling, and the little evil smirk he gives while recalling his master's death shows how creepy he is even before his face gets fried.
Still doesn't diminish what happens later: Obi-Wan Kenobi, alone, almost unarmed, jumps into a room full of battle droids and their commander, who splits his cyborg arms into four to quadruple-wieldlightsabers against Obi-Wan. The duel only ends when Obi-Wan pries open the armor covering Grievous's torso and shoots the remaining organs inside with a blaster, with the following Bond One-Liner:
In the novelization, when Anakin arrives to see Mace and Palpatine fighting, he can only make out the blades of their lightsabers. They're moving so fast that The Chosen One can't keep up with their movements.
When cornered and disarmed, Palpatine fires a torrent of Force lightning at Mace, who deflects it with his lightsaber and throws it all back into Palpatine's face.
Then when Anakin disarms Mace, the now "scarred and deformed" Palpatine kills Mace with another glorious torrent of lightning. While some find this moment extremely narmy, others defend it as one of Palpatine's best moments for his devouring the scenery with such aplomb that it's hard not to let loose and root for him. All together now:
Legends sources give some more insight into that duel: the Sith use a tactic called dun möch, where they taunt and push base emotions into their Jedi opponents, thus disrupting their ability to call on the Force. On the other hand, Windu's fighting style, Vaapad - which he helped invent - has a mental aspect to it that enabled him to deflect those emotions at Palpatine.
At one point, a lone clone trooper takes out two spider droids by jumping on their backs and unloading on them from above. It's easily missed, since it happens while Order 66 is being carried out, but it's a great one.
Let's face it, the culmination of Palpatine's plan. Once the war was won, he would have had to resign or show himself as a Sith... And yet he manipulated the Jedi into giving him an excuse to become The Emperor and have them exterminated. What's more awesome, according to the Expanded Universethe Jedi knew of Order 66: it was one of at least 150 contingency orders to the Grand Army issued for a number of specific circumstances, with Order 66 being basically "I, the Supreme Commander (Chancellor), have proof the Jedi Order has mutinied, Kill 'em All" and Order 65 being "The Supreme Commander (Chancellor) is unfit to issue orders, arrest him and shoot him if he runs". And yet, they were caught flat-footed when Palpatine, using official channels (because he had to identify himself as the Chancellor and Supreme Commander), ordered their own soldiers to assassinate them.
Some for the clone troopers themselves due to sheer Genre Savvyness: they shoot them In the Back with all the necessary firepower and then some (Cody had Obi-Wan shot with an anti-tank weapon); once they kill their commanders, they continue shooting, check the body, and if they can't find it, they conclude it's most likely still alive and start searching.
As a consequence, the fact Yoda and Obi-Wan survived and reached Coruscant, then defeated a ton of clone troops to break into the occupied Jedi Temple.
Yoda jumping from one clone trooper to another to retrieve the lightsaber he had just telekinetically embedded in his chest, then his look of disappointment/resignation after the scuffle.
The whole slaughter of the Separatist council, without Anakin making a sound, is one of the best scenes in the movie, especially when Nute Gunray not only gets what's coming to him but is brutally cut down mid-whiny plea for mercy.
Without seeming to be even aware of it, Vader deflects a blaster bolt that would have hit him in the back, casually sweeping his lightsaber down from his shoulder. This is one of the most subtly effective demonstrations that he is nearly invincible at this point.
Equally satisfying is the fantastic contempt in Palpatine's voice when he commands Anakin, newly-minted as Darth Vader to "WIPE OUT. VICEROY. GUNRAY. And the other separatist leaders." It's a great reminder to the audience that these sniveling characters are still hanging around and haven't paid for any of their crimes yet. Admit it, you were rooting for Anakin in that scene.
And now, the duel we've all been waiting for: AnakinSkywalker vs. Obi-WanKenobi, ending with Obi-Wan hacking off Anakin's remaining limbs. Even better: that's actually Ewan MacGregor and Hayden Christensen throughout most of the fight, not their stunt doubles, with both having trained in the choreography until they could do it together at full speed. On the commentary, Lucas gushes over how amazing it was to watch them during filming. The fact that Obi-Wan wins this fight is a huge moment of awesome for him, despite what it means for the two of them. Obi-Wan fights the Chosen One, the most powerful Force user in the galaxy, and someone he's said before is stronger than he'll ever be, and wins. It's true that Anakin probably isn't in the best state of mind to be fighting at full force, but it's still damn impressive.
Meanwhile, Yoda decides to do what he does best; kick ass, unleash all of the shit, and personally put a stop to Palpatine's reign of terror, starting off with a Force push so powerful that it scares the Sith Lord, but Yoda won't have any of it.
"If so powerful you are, why leave?"
Upon entering the Chancellor's Senate office, Yoda effortlessly disables the two door guards by telekinetically dashing them against the wall without even seeming to notice them, they are so insignificant to him.
Them fighting on the Chancellor's Podium as it rises and brings them to the Galactic Senate Chamber alone is breathtaking. We've seen this place many times throughout the trilogy and now the Big Good and Big Bad are fighting in it. Even though no one is in the room, it gives the sense that everyone is watching whether good or evil triumph.
Even better when viewed as part of the series. Those who know Palpatine know that he is a man who is absolutely in control of everything around him. He never panics, always thinks about a dozen steps ahead and never acts intimidated or worried. And he is running scared for his life from someone he had taunted only moments ago. For the first time in the series, he has met someone he cannot intimidate or bully, someone who will never be swayed by his words or fall under his spell. He has encountered someone who can destroy him and is damn sure going to try.
The best part? Yoda actually wins the fight. He overpowers Palpatine's lightning and proves he's stronger. So strong, unfortunately, that the explosion ends up knocking him away and giving Palpatine time to recoup and get back up while Yoda is injured. Yoda was literally undone because he was too powerful with the Force, which is both really sad and really awesome all things considered.
Notice that the whole reason Palpatine resorts to trolling Yoda by throwing stuff at him is that he doesn't have his lightsaber. The script says that Yoda disarmed him of it, in what unfortunately must have been an Offscreen Moment of Awesome.
Yoda, like all Jedi, is a pacifist. He'd rather talk than fight. In his encounter with Sidious, it's quite possibly the first time he's wanted a fight like this, and it's a good indicator of how far Sidious has pushed him.
This is how it feels to be Anakin Skywalker, forever: You can hear yourself breathing. It comes hard, and harsh, and it scrapes nerves already raw, but you cannot stop it. You can never stop it. You cannot even slow it down. You don't even have lungs anymore. Mechanisms hardwired into your chest breathe for you. They will pump oxygen into your bloodstream. Forever.
Vader and Palpatine observe the first death star being constructed. Vader crosses his arms, and the emperor just stands watching. What an awesome image depicting the evil the galaxy will have to deal with for the next 22 years.
The very ending. Binary Sunset. There could have been no better way to link both trilogies.