Darth Motherfucking Revan preparing to throw down with three badass Jedi, right at the beginning of the game. Bastila may not think Revan can win, and Revan may not say a word in that cutscene, but it's obvious by the way they flourish their lightsaber that they're about to disabuse some notions. At least, until Malak shoots them.
Climbing the ranks of the Taris dueling arena. Though initially the crowds aren't impressed by the Mysterious Stranger's defeat of "Deadeye" Duncan, the PC quickly earns renown as they defeat Ice and Marl and eventually claim the title of champion from Twitch. Then comes Bendak Starkiller, former champion of the arena in the days of death matches who is built up as a Living Legend who gained a reputation as The Dreaded for winning every single death match he walked in and only retired when they were made illegal. A Dark Side option allows the player to challenge him to an illegal death match after defeating Twitch, and everyone thinks they've gone completely insane. Against all odds, the PC manages to kill Starkiller in the death match. This has the side effect of killing the Mysterious Stranger's dueling career, as challenging Starkiller alone was something insane - now who would be mad enough to challenge the person who killed Bendak Starkiller?
Announcer: Bendak is down! It's over! It's over! The fight is over! Bendak Starkiller is down! Bendak Starkiller is dead! All hail the Mysterious Stranger, the greatest duelist to ever grace the rings of Taris!
Sunry's Murder trial on Manaan can be incredibly awesome in a way that doesn't involve fighting. Sunry's a Republic war hero accused of killing a Sith. On the neutral ground of Manaan, this would be very bad for the Republic if he gets found guilty. It's one of the few situations where, assuming you investigate properly, you can completely screw up the Sith directly and they can't do a damn thing about it. Even better, if you perform the trial perfectly, it's so one-sided that the Selkath authorities charge the Sith with framing Sunry, getting you a planet-wide discount on stores. Not bad, especially considering that Sunry is actually guilty!
The best part is how the trial plays out. What you've learned through the investigation actually alters what is a Light Side or a Dark Side act. If you only find out about the frame job, then getting Sunry off is a good act. If you learn that the "frame" job is only to clean up the Republic Intelligence's clean up of the crime scene, then things change. If you lie to get Sunry off, then you earn Dark Side points. If you out the frame job while holding Sunry culpable, you get Light Side points but potentially risk the Republic's position on Manaan. But there is a third option: you can do the job of a truly neutral arbiter, and present ONLY the facts, omitting only the proof that Sunry did the deed. If you never lie, and structure your rebuttals with a mixture of honesty and simple dancing around the truth, then Sunry is found Not Guilty, but you don't get LS or DS points. The Devs Really Do Think Of Everything.
Choosing Mission for the Leviathan escape. She is a fourteen-year-old Twi'lek girl, sporting no special abilities other than a talent for survival. She's got the lowest hit points of your party. She's surrounded by Sith and stripped to her underwear. But she still mouths off to the guard, picks his pocket, then fights and/or sneaks her way through the deck of a Sith warship crawling with trained enemy soldiers to save a pair of Jedi and a Republic war hero. That, friends, is one badass teenager!
Also, choosing HK-47 is really awesome since you start right by the detention center and having a droid rescue you is pretty sweet. Even Carth comments saying you deserve a medal for what you did. Even more badass if you choose T3-M4, a freakin' utility droid rescuing war heroes and taking out an entire group of Sith Soldiers with two simple pistols!
While Jolee's escape is much funnier than awesome, it's still awesome having an half-naked old man Mind Control and Troll a guard for all he's worth and either take on other guards head on or sabotaged them.
Juhani's rescue has her using her unique ability* Using the Force Camoflague ability to go into stealth mode without needing a stealth unit to hide from the soldiers searching the Ebon Hawk, and making her way through the prison level. Additionally, once Carth, Bastila and the PC are freed, Bastila states that Juhani is more than deserving of the rank of Jedi.
The last line you get to say before dueling Darth Malak on the Leviathan has the potential to be a crowning moment - you can (and probably will, if you're going Light Side) say "Your power is no match for the light!" Consider it: The Reveal has just occurred - you were Darth Revan. You have every reason to flip out, because everything you know is wrong. And yet, in light of the universe lying to you, in light of discovering that you were a Dark Lord of the Sith, you can still stand fast to your beliefs and proclaim that you now stand with the light, you will never fall into darkness again. That's pretty damn inspirational...
There's an equally awesome line you can say to Malak if you've decided to go Dark Side: "I am the TRUE Dark Lord of the Sith! Now bow down before me!"
The above line actually can be used several times in the game, not just on Malak.
And, in case you want to play it nicely neutral before going either way, as Malak starts gloating about his apparent victory, you have the option of saying "You seem to have forgotten that I'm still alive, Malak!" This line reminds one of Luke in Episode V, where he cockily tells Vader that he's "full of surprises".
Malak saying he expects that all his apprentices and the droids of the Star Forge will not kill you, but hopefully they will slow you down.
Malak gets that with you in the Light Side ending along with a Heartwarming Moment. Revan tells him they're sorry they led Malak to the Dark Side; Malak tells them that it's not Revan's fault, he chose to walk down that path and in the end "I am nothing".
"The apprentice has learned his final lesson."
Playing a "light side" character on the Sith homeworld of Korriban. After infiltrating the Sith academy and watching in bemusement as Master Uthar and his apprentice Yuthura attempt to use you as their pawn to betray each other, the player is given an ultimatum by both as to which one the player will support against the other. Answering, in effect, "I choose neither. I'm not a Sith, you idiots, I'm a Jedi." and then beating both simultaneously — and then, as frequently as not, the entire rest of the Sith Academy — ought to dispel any lingering questions about the ability of good guys to be badass. One of the most joyfully righteous and satisfying moments in RPGs.
Even better, side against Uthar and convert Yuthura back to the light side if you talked to her earlier about why she joined the Sith in the first place. She runs off to the Jedi Academy on Dantooine if it hasn't been blown up yet, leaving you to kick the rest of the academy's collective ass. And that's not even counting the opportunities to mock and sabotage the Sith's efforts earlier on the planet. Basically, Jedi!PC on Korriban demonstrates why the Sith shouldn't assume Jedi are incapable of deception.
Fine, let's count the opportunities to mock and sabotage the Sith before. Converting Mekel, Dustil, Kel, and Yuthura to the Light and the plain desertion of Dak. Killing off the rest of your class that you don't redeem. Facilitating the escape of defecting Sith students and a droid. Conning Uthar into giving you credit for exactly this. Redeeming effing Ajunta Pall three millennia after his death. And this is ignoring the students you kill beforehand and the fact that you wreck the entire academy top to bottom afterwards. Awesome indeed.
The example of Ajunta Pall is especially awesome as he is listed in Wookieepedia as being the very first Sith Lord. Anyone can be redeemed, indeed.
Hell, even your companions can get in on putting down the Sith. Of note, JoleeBindo can let out a stellar dig that doubles as one of the game's funniest bits. Having Canderous there as well gives an added bonus.
One other satisfying example is sticking it with a fellow student in the Sith Academy. From the start you know you're not going to like him: he calls you "freak" and boasts of killing you, among other things. Then along comes the tomb of Ajunta Pall, which gives you three swords, of which one belongs to Ajunta Pall himself, and you have to figure out which is the real one. You're about to exit when this student comes along and tries to bully you into handing over the real sword, intending to get the credit of finding it for himself. Naturally, you can kill him, but that's not as satisfying as giving him one of the fake swords and returning to the Academy to see Master Uthar Force-choking the student to death for failing to verify the sword's identity. And you get no Dark Side points from it! Sure, you do lose the (fake) sword, but there are better weapons out there.
When kidnapped by Uthar's crazy predecessor Jorak and forced to play a twisted pop quiz, a Light Side PC can deliberately answer every question wrong in the knowledge that they can take whatever punishment Jorak dishes out (especially if they specialized in Force Heal), while the other student who would be punished for the PC's right answers can't. This impresses the other student to the point where he proposes working together to bring Jorak down, something that would be unthinkable for a Sith. Sure enough, if you take him up on it, he converts to the Light Side afterwards.
A PC that has embraced the Dark Side deep enough can actually beat Jorak on Korriban at his own little game by giving the right answer to a trick question he technically has no way of knowing.
Neither. A true Sith never dies.
A Dark Side PC can also choose to manipulate both Sith Masters against each other then kill them both. Afterward, (if done after the Leviathan mission) the PC can proudly proclaim themselves as Darth Revan as the Sith Masters fall.
On the Star Forge when Malak sends his entire army to attack you. This is an awesome moment because he admits that he has no hope of them killing you: he's only doing it to slow you down while he prepares for the final showdown.
The Dark Side ending. The main character as the returned Darth Revan sending out an effectively infinite, invulnerable fleet of Sith ships to conquer the last remnants of the Republic, led by an apprentice who will guarantee victory in any battle, all to a marching tune of Palpatine's theme. Galactic Conquest never looked so good.
If you're light-sided, the ending is just as awesome! Standing with your True Companions under a clear sky, everyone smiling, Dodonna and Vandar congratulating you. Your party waves to a cheering crowd... Good Feels Good!
Just the fact that the Republic's highest honor is being awarded to two droids, including Revan's personal murder bot, a Wookiee, and the future Mandalore is definitely worth a cheer.
The devastation of Serroco is mainly a huge tearjerker, but there is an awesome moment for Gryph and Slyssk. In panic, Slyssk grabbed Gryph, boarded the nearest ship and took off. The action saved an entire batalion of republic soldiers, and "Benegryph Goodvalor" and his trusty trandoshan sidekick soon became known as the Hero of Serroco, hailed as a great hero of the Republic, and star of countless propaganda holos.
Also from Serroco: Carth Onasi, unlike his commanding officer, listened to Zayne's warning, and used the old tornado warning to save the native Stereb species from the nuclear bombardment; He managed to call seventeen cities, and saved countless lives.