The Tranquil Fury he exhibits as he cuts off Sidious is also pretty awesome, because you know that for the first time in six movies, Yoda is pissed.
"If so powerful you are, why leave?"
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.
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.
The whole slaughter of the 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.
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.
The novelization's version of the scene where Vader wakes up on the slab is wonderfully nightmarish. Here, take a Vader Breath:
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.
Even with the Big "NO!", the scene where Vader awakens is actually quite chilling.
Obi-Wan's triumph over General Grievous is probably the character's single most badass moment in the film, and he even gets a Bond One-Liner: "So uncivilized."
Better yet, at the start he is alone, has almost no weapons and no guarantee of success. And he fights anyway without showing any fear. At that moment, Alec Guinness is no longer his goal. Ewan McGregor has just proven himself a worthy successor to Harrison Ford.
The opening. We see a Republic battleship floating over Coruscant, then the pair of starfighters Obi-Wan and Anakin are in fly over it, skimming the dorsal surface before executing a perfectly synchronized barrel roll... right into a massive space battle.
Hell the entirety of the Battle of Coruscant counts as one, we see something like 100 Republic and Separatist battle cruisers scattered around above the orbit of Coruscant going at it and most likely about a couple hundred to maybe a thousand clone and droid star fighters chasing each other around in one large massive space dogfight. And to top it all off, Anakin and Obi Wan flew straight through all of that without getting shot down, managed to finally kill Count Dooku, got the chancellor out alive, and successfully landed half a battle cruiser and came out with barely a scratch. As Obi-Wan says when they touch down on Coruscant, "Another happy landing".
Artoo destroying the buzz droid that landed on Anakin's fighter, with some advice from Obi-Wan. Even better in the novelization where Artoo busts out every tool on his person and leaves the buzz droid in pieces.
All of Anakin's piloting stunts, but the crowning one is his successful landing of the broken-off bow of the Invisible Hand. Quoth the novelization: "This is, put simply, impossible. He's going to do it anyway."
The novelization had another one during its introduction, when describing Obi-Wan and Anakin making their appearance.
There's no post-production speeding-up of the fast-paced climactic melee between Obi-Wan and Anakin in the end; Ewan McGregor and Hayden Christiansen got so skilled from years of lightsaber training and filming, both from this film and Attack of the Clones, that they could indeed duel at the pace you see on film.
R2-D2 takes down TWO Super Battle Droids. With just his wits, an oil slick, and a pair of rockets. I want him on my side.
Grievous escaping by smashing a window and exposing the entire room to the vacuum of space. As smug as he may be, that takes balls.
Or, in his case, complete lack thereof.
Palpatine versus Mace Windu... and Mace wins.
A combination of Awesome and Tear Jerker: Darth Vader taking his first breath.
Obi-Wan and Anakin's fighting styles. They've been at war for a good three years now, and know exactly how to kill the highest amount of enemies with the least amount of effort. Back in the first two prequels, being surrounded by battle droids was a serious problem. Now, it's a minor inconvenience.
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 Clones 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.
Palpatine's Jedi Trap at Utapau is his Crowning Moment of Magnificent Bastard, which the novelization sums up.
First, he picks a planet way out in the Outer Rim that he could care less about, but has geography that helps funnel the action into certain areas, making it easier to predict.
Second, he baits the trap with something that will guarantee the Jedi will rush in. This bait is General Grievous, whose death or capture would end the war and Palpatine's emergency powers, two things the Jedi desperately want.
Third, he makes the trap's Jedi-killer the same as the bait, guaranteeing that even should the Jedi spot the trap they will continue to put themselves in its teeth of their own volition.
And lastly, none of it really matters because the true purpose of the trap is to ensure the Jedi is out of the way for Palpatine's real move. Or in other words, to make sure Obi-wan isn't around to keep Anakin from falling.
The quiet opening, a single Star Destroyer rolling across the screen to the sound of lone drumbeats. Two small fighters race across the screen, and the most bombastic and cheer-inducing take on the Force Theme ever blares across the screen. We know exactly who these two Jedi Knights are, we know exactly what they're about to do, and we know in the space of a single scene that this is the movie we've 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."
The Battle of Coruscant was one big Moment of Awesome for Anakin. He tricks two high-quality homing missiles tailing him into blowing each other up. He is able to pilot his interceptor with such precision that he crushes one of those tiny little buzz droids between his fighter and Obi-Wan's, causing no damage to either vehicle and utterly destroying the droid. And he does this at the risk of getting a buzz droid on his own fighter. When told the hangar shields are still up on the Invisible Hand, he isn't worried at all. He just blasts the generator like nobody's business. Later, he kills Dooku in what quickly becomes single combat. After that, he carries the unconscious Obi-Wan on his back like he's as light as a rag doll, and finally, he safely crash-lands half a cruiser that was never designed to be able to land safely.
The duel with Dooku is made even better in the novelization. It's told from his perspective, and it shows him going from a complete Smug Snake through his Oh Crap! moment when he realizes that Obi-Wan and Anakin aren't fighting like he expected to his final realization of his betrayal by Sidious.
And his realization, after taunting Anakin, why Sidious wants him as an apprentice: the boy is half-Sith already. Immediately following, he taunts Anakin again, this time to deprive him of Dark Side power, only to have Palpatine encourage him. Dooku immediately wonders "Whose side is he on?" Well, Count, you're about to find out...
"Under the circumstances I'd say the ability to fly this thing is irrelevant."
Obi-Wan has two: defeating (along with Yoda) an entire clone trooper company, and chopping off three of Anakin's limbs with a single strike.
The entirety of his final duel with General Grievous on Utapau, but especially the climax which saw him hanging over a ledge and he used the Force to shoot the general with a blaster (complete with irreverent comment afterward)? When Luke's hanging over a precipice, it means he's had the stuffing kicked out of him, and he's barely going to survive this encounter. When Obi-Wan is hanging over a precipice, it means he's about to kick ass.
Obi-Wan (teaching Luke to use a lightsaber): "Not as clumsy or random as a blaster. An elegant weapon, for a more civilized age."
Let's make that victory in his fight with Anakin clear - Obi-Wan fights Anakin Skywalker. Darth freaking Vader. One of the greatest film villains of all time. Stronger with the Force than Yoda, and everyone says that he'll be the one to bring balance to the Force. In his prime. And Obi-Wan fights him and wins. Hell, he walks away only looking a little battered.
Windu also gets one in Revenge of the Sith, in his duel with Palpatine. He even would have won, had Anakin not shown up. The dialogue that preceded was also awesome (for both!):
Mace: In the name of the Galactic Senate of the Republic, you are under arrest.
Palpatine: I am the Senate!
Mace: Not yet!
Only Palpatine was most likely toying with Windu the whole time, as he had just butchered the three other Jedi Masters.
The above dialogue is even better in the trailer:
Mace: In the name of the Galactic Senate of the Republic, you are under arrest.
Palpatine: Are you threatening me, Master Jedi? *Ignites lightsaber and lunges. Cue the most badass and ominous music ever used in a Star Wars trailer*
Ah, but then we would not have seen Palpatine become the Large Ham he was born to be. Palpatine announces the birth of The Empire and the death of freedom to the Senate... who respond with a standing ovation. Your Majesty, your ascent to Magnificent Bastardhood is complete. The horrified-sounding ominous chorus in the background doesn't hurt, either.
While some find this moment extremely narmy, others defend it as one of the best, if not the best, Palpatine moment when he starts devouring, and we mean devouring, the scenery with such aplomb that it's hard not to let loose and root for him. All together now:
Palpatine:POOOWEER! UUNLIIIMIITEEED POOWWEEEER!!
That duel is explained in the EU. The Sith like to use a subversive tactic called Dun Moch, where they mock their Jedi opponents and telepathically push base emotions into their minds, which disrupts their ability to call on the Force. That's why Palpatine laughed at Yoda and hissed at Mace Windu. The mental aspect of Windu's fighting style allowed him to reflect those emotions back at Palpatine, while Yoda had no such defense. Mace had legitimately defeated Palpatine until Anakin showed up. And Mace lived while the other Masters died because his style, Vapaad, made him the absolute best duelist in the galaxy, possibly the best throughout the franchise's entire canon history. Only Dooku and Yoda ever fought him to a standstill, and that was before he made a style so vicious and powerful that an uncautious user would be drawn into the Dark Side. No telling what a Sith could do with it, but Vapaad died with Mace. He actually had to kill the only other two people he taught it to because they couldn't handle it.
In the novelization, it's stated that Palpatine and Mace stalemated, with Anakin being the one to decide the outcome. At one point, Anakin observes and can only make out the blades of their lightsabers, they're moving so fast that The Chosen Onecan't keep up with their movements.
Yoda's decapitating of the clones about to kill him on Kashyyyk. One moment, he's on the floor, seemingly defenseless after feeling the deaths of so many Jedi, and the clones are readying their blasters. The next, the clones are lying dead on the floor and Yoda is deactivating his lightsaber.
How about the fantastic confrontation in Palpatine's office?
Palpatine: At last the Jedi are no more...
Yoda: Not if anything to say about it I have! *Force pushes Palpatine so hard he goes flying across the room and lands ass over head*
Yoda: At an end your rule is... and not short enough it was.
The fact that the unflappable Palpatine tries to run away rather than fight is a good indicator of how badass Yoda is.
"If so powerful you are, why leave?" (Draws and ignites lightsaber )
Before that, Yoda casually knocks out Palpatine's two guards with a wave of his hand.
Heck, the entire Obi-Wan vs. Anakin and Yoda vs. Palpatine sequence in Revenge of the Sith was a Crowning Moment of Awesome. Especially considering the former was done in real time, no speed-up required.
According to the special features on the DVD, when Ewan McGregor and Hayden Christensen finished their fight, the entire crew broke out in applause.
In the Yoda vs. Palpatine fight, when Master Yoda takes that first step to shove the two massive great blobs of Sith lightning back at the guy that fired them, there's a moment, just a moment, when you think that, despite the Foregone Conclusion and all, he might still win, somehow, because he's so awesome he can somehow overwrite Real Life history.
A small moment, and one easily missed as it occurs between scenes of Order 66 being carried out, but an example of why Clones aren't just cannon fodder: a single clone trooper takes out two spider droids, where previously they had been annihilating entire squads in seconds, by jumping on their backs and shooting them at full auto from above.
At the end, all it took was Vader taking one deep mechanical breath and every hair on your body stood on end, followed by one of the most heartwrenching Big No's ever. 
Or the look on Vader's face as the mask lowers, eyes widening as he realizes what his world will look like from then on...
Them fighting on the Chancellor's Podium as it rises and brings them to the Grand Convocation 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.
Say what you will about Anakin, but marching up the steps of the Jedi Temple at the head of the entire 501st is pure win.
Obi-Wan, alone, nearly unarmed and without backup, facing up to a room full of bad guys including one with four Lightsabers. Han Solo would be proud.
His entrance in that scene: "Hello there." Best entrance ever. Then dropping that huge thing on Grievous' guards. Then strolling on, twirling his lightsabre like a walking stick.
Grievous: "I've been trained in your Jedi arts by Count Dooku." Obi-Wan might have been thinking: "Good, because I trained the Jedi who killed Count Dooku." (In the movie, he might be thinking it. In the novelisation, he says it in his own inimitable Deadpan Snarker way.)
More: he wasn't trapped, ambushed, or backed into this situation. Obi-Wan Kenobi saw a huge hangar filled with droids, and with General Grievous, went "Hmm", and jumped down into the middle.
Though Grievous having four arms was slightly spoiled by the cartoon miniseries that bridged Episode II and Episode III, you have to admit that the way he advances towards Obi-Wan on Utapau, four lightsabers in his hands, all four of them spinning like saws as they carve up the floor, is a hell of a way to start a duel.
Let's face it, the entire movie is a CMOA for Palpatine...and more specifically, for Ian McDiarmid. If his performance as the character wasn't already legendary before, it certainly is now.
Obi-Wan's: "Let her go Anakin! Let. Her. Go." Even in Anakin's deranged state of mind, corrupted by evil, and filled with hatred towards both his wife and his former Master, he listens. Obi-Wan is here, and his very presence demands that respect.