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In the first game with certain mods installed, the battle against the Chill and the Black Talons mercenaries in the bandit camp can become very difficult so, winning the battle is one Moment of Awesome without a doubt! Your party who may have made up of just Level 5 or 6 adventurers just beat a small army.
The protagonist gets one of their own (or can) in the first game when talking to Portalbendarwinden. After hearing all of the word salad coming out of his mouth, the protagonist can consider it a rant-inducing slight and scream at him. It is very satisfying after being the errand boy or girl of the entire Sword Coast all the way from level one up to the XP cap to be able to tell Portalbendarwinden to just give them a straight answer. (If you do pick this option, Portalbendarwinden does give you a straight answer, in the form of telling you that you're a jerk, he's not talking to you anymore, and disappearing without you being able to complete the quest. Doesn't stop the option from having some catharsis, though.)
"Ok, I've just about had my FILL of riddle asking, quest assigning, insult throwing, pun hurling, hostage taking, iron mongering, smart-arsed fools, freaks, and felons that continually test my will, mettle, strength, intelligence, and most of all, patience! If you've got a straight answer ANYWHERE in that bent little head of yours, I want to hear it pretty damn quick or I'm going to take a large blunt object roughly the size of Elminster AND his hat, and stuff it lengthwise into a crevice of your being so seldom seen that even the denizens of the nine hells themselves wouldn't touch it with a twenty-foot rusty halberd! Have I MADE myself perfectly CLEAR?!"
In the first game, if you have maintained a normal-to-high Reputation, your final dream states that you have overcome and mastered the taint of Bhaal within yourself. Plus, it throws in a free ability for good measure.
Saverok actually deserves Villain Cred for the fact his plan is actually one of the more interesting ones in gaming. He creates an iron shortage and manipulates Medieval economics using laws of supply and demand for war, ups tension with Amn and Baldur's Gate, undermines the existing nobility, and eliminates his own rivals for power in the Iron Throne before preparing to become Grand Duke of Baldur's Gate with popular support. This alone would be a big deal but it's all a smokescreen for his plan to kill thousands of people in war to empower himself as a Bhaalspawn to ascend to godhood. It almost works too.
Specifically, you get also get props for thwarting the plan by doing a lot of Medieval investigation work. You can't just beat Saverok by killing him but have to dismantle his operations piece by piece. A lot of it involves politics, making alliances, and striking at his source of wealth.
Baldur's Gate: Siege of Dragonspear
The Bhaalspawn protagonist starts off having achieved a life of fame and fortune, living in the Ducal Palace as a permanent honored guest. It is the perfect end for an adventuring hero, right up until the assassins ruin it.
Caelar Argent has managed to create a people's crusade through nothing more than her raw charisma and conquered a significant chunk of the Sword Coast. This is all part of her larger plan to invade the Nine Hells to rescue the damned.
The Bhaalspawn protagonist and their party can end up slaying a dragon in direct combat mid-way through the game and claiming its treasure horde. The mark of the ultimate adventurer as an Optional Boss.
Even bigger as an accomplishment is the chance to slay Gurn Coldheart, a dwarven lich who has recently been created. Defeating it in direct combat is possible but highly unlikely at your level but you can exploit its weakness to dwarven holy magic to weaken it. Even that isn't enough, though, and you must toss its Soul Jar into a portal to the Elemental Plane of Fire.
Baldur's Gate II: Shadow of Amn
In the sequel, when you infiltrate a Drow city in order to both learn more about Irenicus' alliance with them and save a silver dragon's eggs, you're able to talk down an Aboleth that threatens to expose you.
In BG2, most of your party members throw out some pretty good lines before the final battle with Irenicus (including a surprisingly good one from Aerie).
Minsc: I grow tired of shouting battle cries when fighting this mage. Boo will finish his eyeballs once and for all, so he does not rise again! EVIL, meet my sword! Sword, MEET EEEEEEVIIIIL!
Jan Jansen (Yes the Cloudcuckoolander gets one): Some villains refuse to die. Kill 'em once, kill 'em twice, they just keep coming back. It's just like a bad play. Here's hoping for a decent ending...
Jaheira: No more platitudes, Irenicus. You have taken much from all of us. Now you die your final death!!
Edwin (in one of his rare badass moments): Power is on our side, sorcerer! You cannot hope to defeat us in this final reckoning! Your end is near at hand, wail if you must!!
Aerie takes several levels of spunk in Throne of Bhaal, but especially if she's in a romance with you. Midway through her romance, she becomes pregnant with CHARNAME's child, yet opts to keep travelling and fighting alongside you. Better yet, wait long enough and she'll give birth, quietly patch herself up with a few healing spells, and continue on as normal. Pregnant Badass indeed.
Even better: The baby itself is an inventory item. That means by the end of the game, you are invading dragon's lairs and hellish demiplanes with an infant strapped into mommy's backpack.
Deciding to stay mortal instead of ascend to godhood is pretty badass.
Also, the protagonist has some badass quotes, by courtesy of wikiquote:
"Poor little gnome. My heart bleeds. Yours will too."
"Fine, I'll do all the actual work. As usual."
"We all know this is going to end in violence. Let's just cut right to the good stuff."
That part when asked by Elvish general if you fled Drows, you can answer that no, you left them broken, you did not "flee".
In the second game, The moment when Jon Irenicus breaks out of Spellhold and slaughter his would-be jailkeepers. If you haven't played the game, then you won't understand how tempting it is to just write "Anything he does" as a Crowning Moment Of Awesome, but that's the one that stands out the most. Here, have a link
Jon Irenicus: I cannot be caged. I cannot be controlled. Understand this as you die, ever pathetic, ever fools!
The first time that Aerie started using the battle cry "This will hurt you a lot more than me!" Incidentally, she was armed with the Crom Faer at the time.
Jan Jansen: Whoa! This place looks just like... it reminds me of.. this is just like that time I... hm. I don't think anything like this has ever happened to me before...
Baldur's Gate 2: Throne of Bhaal let you witness your character raised to Champion's League of awesome, for example, having vampires attacking you only to have a Rousing Speech.
Baldur's Gate II: Throne of Bhaal
Think about what CHARNAME achieves in the defeat of Yaga-Shura - s/he single-handedly (well, up to six-handedly) broke through the lines of an entire army and defeated its leader, who up until mere hours before their arrival was literally invincible (and few people would have known that that was no longer the case, up to and including Yaga-Shura himself). The stuff of legends, indeed.
Indeed the PC has multiple opportunities to take on entire armies in Throne of Bhaal. Cast Timestop, three "Horrid Wiltings" and rejoice as platoons of drow spontaneously combust into clouds of splattering gibs!
From the popular Ascension mod, going up against Abazigal's entire family of dragons — at the same time — and winning (ornot, as the case may be).
Defeating Amelyssan at the peak of her power no doubt counts. Bonus points for playing the Ascension version of the battle, where you get to defeat the rest of The Five (or four of The Five plus Gromnir if you take a certain option) all over again!
Sarevok (the Big Bad of the first game) is so badass that even being killed - TWICE - couldn't stop him. He returns in Throne of Bhaal as a playable character, and doesn't even suffer from Good Is Dumb.
Sarevok: "I live! Flesh and blood and bone! I AM ALIVE! HAHAHAHAHA! I swore I would scratch and crawl my way back into the world of the living, and I have DONE IT!"
Sadly only comes up in the Throne of BhaalAscension mod, but the dialogue with Balthazar has some potentially awesome outcomes. Not only can you completely ream him out, doing so is the most effective way to persuade him to stand down or even recruit him. It's especially cathartic if Charname is a good guy themselves and has taken the time to help the people of Amkethran.
Charname: You don't honestly see yourself as the force of righteousness in all this, do you?
Balthazar: I make no judgement upon you, <CHARNAME>. You are what you were born to be. I can only trust myself to hold to the path of good that will lead to the destruction of the true evil that threatens Faerun. There is no other path for me.