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. Credit also goes to how, when the Federation brings in another blast door, he basically just shrugs and keeps cutting.
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 a 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 Establishing Character Moment for the droidekas. The Jedi have just carved their way through the battle droids with ease, and then these two droids show up. It's an honest-to-goodness stalemate - the Jedi aren't in an danger of being killed, but there's no way in heck they can destroy the droidekas.
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. It's a move Obi-wan's apprentice would later attempt, with far less successful results. Maul had the high ground, but even that wasn't enough to stop Obi-Wan.
The fact that 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.
Obi-Wan's badassery is shown even earlier as well. Despite Maul holding off him and Qui-Gon simultaneously, Obi-Wan shows no fear when his master falls behind, calming striding towards Maul and nonchalantly twirling his saber. See it here.
It should also be noted that, odd Dark Jedi aside, no Jedi has fought a lightsaber-wielding opponent for a thousand years, and most Jedi wouldn't have practiced much with double-bladed lightsabers. Here, Qui-Gon and Obi-Wan do pretty darn well against a foe they're completely unfamiliar with.
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 Knightley, 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.
Padmé: Now, Viceroy, we will discuss a new treaty.
Never mind for just a moment how annoying young Ani 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. Little Anakin destroyed the Droid Control Ship with nobody but R2-D2 backing him up.
Anakin: Qui-Gon told me to stay in this cockpit, and that's what I'm going to do! (later, they blow up the ship's main reactor core with several torpedos)
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 them breaking and running is less a rout and more a tactical scatter to make the enemy artillery fire as ineffective as possible. Losing the shield means the Gungans are down, not out.
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)."
The opening notes of "Duel of the Fates" adds to this, signaling that the Jedi are in for the fight of their lives.
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. 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.
Additional credit should be given here to the sound design, which not only emphasized the incredible speed and power of the pods, but also made each one distinct in its own way, from Ani's high-pitched, jet-like screaming to Sebulba's low, pulsing sound similar to a speedboat.
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.
Meta example; the sheer hype that built up to the movies release. Regardless of the films divisive reception, you could not have experienced a more highly anticipated movie in the entire history of cinema. To put it in perspective—in the early to mid 90's, Star Wars was remembered fondly, but was basically a modest niche for kids and nostalgic fans, and nobody believed that there would ever be anything more coming out for the series outside of tie-in product like Shadows of the Empire. But once word got out that after a decade and a half of waiting, not only would the original Star Wars movies get a theatrical re-release, but a brand newStar Wars movie, with the original maestro taking the directing helm, was coming to theaters, the entire planet lost its collective shit. There have been stories of people going into theaters to see movies justto see the legendary 1998 teaser trailer attached to them. The trailer later became the first released online, and it was downloaded 3.5 million times in the first five days, and to 6.4 million in three weeks, mostly through slow-as-molasses dial-up internet which could take hours to download. There have been stories of people camping out for weeks outside of theaters just so they could see the premiere of the movie. Some people even flew in another country just because The Phantom Menace was premiering in the US first, and they didn't want to wait to miss its premiere or wait for it to show up in their country. The sheer anticipation and idea that the world was going to see a brand new Star Wars movie could be felt everywhere you went in the nineties, in every neighborhood, fan club and toy store or just plain store. Love or hate the movie, the buildup to its release was truly a once in a lifetime event. In fact, an entire bookhas been written solely about the history of the buildup to the movies release. What other movie in history can lay claim to that?