A small one. When Obi-Wan, Qui-Gon and the Queen's forces open the door and see Darth Maul there, all of the Naboo Guards put their weapons up and looked scared out of their mind. Watch Captain Panaka. He just looks as calm as ever and levels his blaster at Maul. The only reason he leaves is because the Queen told him to. That man is a badass!
Qui-Gon has three of these moments:
When he's cutting up, then melting down the blast door, while the Force Theme plays on the soundtrack,
When, after Maul knocks Obi-Wan off a catwalk, Qui-Gon responds by hip-checking the Sith, then pimp-slapping him off the same catwalk, which just screams "No one touches my Padawan!"
And when the three of them are separated by the energy walls, Maul is pacing like caged tiger, Obi-Wan is anxious, and Qui-Gon simply kneels down to rest and meditate, utterly cool in the face of impending combat.
A perfect microcosm for the differences between Jedi and Sith, as well. The Jedi Master is serene and patient, the Sith just wants to kill something.
The Qui Gon/Obi Wan/Maul duel is the best choreographed fight in both trilogies.
Awesome Music: The Darth Maul/Qui-Gon/Obi-Wan lightsaber battle music (Duel of the Fates) has become a marching band staple.
Even a significant number among the many, many people who despise this movie admit to loving this particular battle, it is that good.
Made even better by the fact that the Obi-Wan/Darth Maul part of the fight, up until Obi-Wan is thrown into the pit, is completely silent. There's no music, only the sound of lightsabers and battle. It adds weight to the entire scene.
Obi-Wan using the Force to not only pull himself out of the pit but also grabbing Qui-Gon's lightsaber and then flipping over a stunned Maul and cutting him in half. When Qui-Gon told him earlier he would be a great Jedi knight, he wasn't kidding.
The fact hat he overpowers Maul for a while counts as well. He's up against an opponent superior to him in both swordplay and physical power, is battling against grief and anger that are trying to pull him to the dark side (if I remember correctly, the novelization touched upon this) and that he manages to channel all this to be stronger than before shows how much potential he still has.
The fact that she did this solely to create a distraction and draw off most of the guards, allowing her captured Queen to go for the blasters hidden in the throne and subdue the remaining Trade Federation leadership.
Made even better with the fact that the handmaiden in question is none other than Keira Knightly, being an Action Girl before she became a big name.
The blasters in the throne themselves. The Naboo may be peaceful, but they are Crazy-Prepared.
Never mind for just a moment how annoying young Annie could be, the external shot during his Outrun the Fireball scene, with the Trade Federation battleship being engulfed in flames as it is gutted by an internal explosion, as the Naboo pilots remark that nothing they did yet could be the cause. The Force theme swells, and the pilots break out in cheers as they see one of their fighters shoot out of the hangar just as it erupts in explosions.
When Padme finally reveals herself as the Queen in disguise, everyone looks shocked...except for Qui-Gon, who crosses his arms and gives a glorious shit-eating grin as if to say "Called it!" Retroactively makes all his lines to Padme the handmaiden that much more awesome, since the whole time he was Trolling the Queen about her Paper-Thin Disguise.
Made even better by him looking at Obi-Wan who has a look that basically says "I'll pay up later."
A kickass poster at time of release was of Anakin walking across Tatooine as his shadow cast is that of Darth Vader. Even better is that it was drawn by legendary poster artist Drew Struzan.
At least one variant shows the ominous tagline "Never look back".
The fact that a voluntary security force managed to overpower the Trade Federation counts as one.
The fact that the Gungan Army-made up of volunteers and a few veteran guards and militia men- was able to give the Trade Federation a fairly even battle. This 'band of primitives' manages to hold their own against a vastly superior force, only breaking and running when their force field is finally broken.
Even if you were spoiled to hell and back by the advertising blitz beforehand: when that door opens, and Darth Maul is standing there looking like Satan himself — and he busts out the double-bladed lightsaber —was there any other reaction than, "Holy crap"?
What happens directly after Maul shows up adds a lot to the awesomeness. When the doors open to reveal Maul, Amidala and her troops look good and ready to wet themselves, until the Jedi step forward...
Qui-Gon Jinn: "We'll handle this."
Amidala:(who can't wait to get the hell away from Maul) "...we'll take the long way (around)."
Obi-Wan out of the gate vs Maul.
When Obi Wan jumped out of the shaft in the Theed palace and chopped Darth Maul in half.
Minor example: "I will not condone a course of action that could lead us to war."
A bigger one later: "I will not defer. I've come to you to resolve this conflict now. I was not elected to watch my people suffer and die while you discuss this invasion in a committee!"
Padme and her handmaidens really can't be separated in this episode; a CMOA for one of them is a CMOA for all of them. That being said, Sabe's quick thinking and ability to keep her cool when the slightest misstep will spell all of their deaths and she's not able to openly consult with her queen? Badass Normal.
Openly consult? No. But they clearly have a code established. When Qui-Gon is asking the "Queen" to come to Coruscant, and Panaka is asking her to remain on Naboo, Sabe says that "Either choice presents grave danger. . . to us all," while turning to Padme, who replies "We are brave, Your Highness." A seemingly innocent phrase, but clearly a verbal code to let Sabe know which choice the real Queen was making.
The pod-race finale. Sure, it was more the folly of Sebulba rather than direct actions on the part of Anakin, but just watching Sebulba's ginormous pod engines smash into an oncoming rock at 500 MPH as Anakin's tiny little thing cruises majestically on by was certainly a Crowning Moment of Awesome.
Little Anakin taking down the Droid Control Ship with nobody but R2-D2 backing him up.
To those who were sufficiently well-read in Star Wars lore to recognize his name, The entire film was a Moment of Awesome for Palpatine: manipulating events to get himself elected Chancellor, as the first step in taking over the galaxy.