Jack battles and destroys virtually an entire graveyard full of zombies by himself.
The Scotsman's Wife punches an elder Celtic Demon in the crotch and headbutts him, then follows up by ripping the entire demon army to shreds with her bare hands, and in a couple of cases teeth.
The battle in "Jack and the Spartans" had the Determinator Spartans shoot missiles from the spears and robotic minotaurs that could repair themselves endlessly. The final battle of said episode had Jack throw his sword to the Spartan leader and shows that even the Spartan leader could use a katana pretty well. It ends with Jack sacrificing his life to save the Spartan Leader.
Also, there is a scene with the Spartan King stabbing one of the robots in the back, pulls off its arm, AND PROCEEDS TO BASH ITS HEAD WITH ITS OWN ARM.
And just after that? He punches a robot. In the face. Bare-knuckled. And seeing as the robot is still embedded around his fist, he lifts it and shakes it off, into a bunch of incoming robots, blowing them all up.
Any battle featuring both Jack and the Scotsman is considered awesome because it serves as a way to compare their different fighting styles.
The third episode of the show - also the last third of the Compilation Movie that served as the show's pilot - cuts to its mid-episode break as Jack and the sentient dogs he's trying to free finish preparations for fighting Aku's incoming robot horde. When the break is over, the show gives us the fight between Jack and the robot horde...a fight that lasts for nearly ten minutes, features very little dialogue, and is generally one awesome moment after another for Jack.
After Jack has single-handedly reduced an entire army of ceaseless beetle drones to a scant handful, he stares the remaining forces down while soaked in oil (their blood). Then one of these unstoppable battle robots (that probably aren't programmed to understand what retreat even MEANS) hesitates... and takes a step backwards.
Episode XLIV: Six of the world's greatest bounty hunters end up in the same place to try and take down Jack. They all ambush him at the same time. Jack utterly defeats all of them in the time it takes a drop of water to fall from an icicle and hit the ground. One bounty hunter is still alive/conscious and draws her back-up weapon, a small knife. Jack stands motionless, with his back to her; realizing the futility of attacking Jack, she drops the knife and then drops to her knees. Jack walks on down the road, having not said a word during the entire episode.
This one may be based on a Lone Wolf and Cub story, interestingly; certainly there's a very similar sequence in that series, and they weren't too shy about indicating at least some LWC influence on Samurai Jack...
"No. Jump Good." It's the (episode-long) setup that sells it.
At least two earlier in that episode, when the results of the training are demonstrated: Jack removes his training weights and just... ascends, and the "peaceful villager" ape tribe give their foes a humiliating defeat, warning them never to return.
Samurai Vs. Ninja. The ninja hides perfectly in darkness... so with the angle of the sun temporarily turning everything into either pitch-dark or blinding white light, Jack refashions his kimono into pure white ninja garb and proceeds to fight fire with fire.
The entire episode of fighting with the blue guardian of the time gate. One of the most epic battles and also one of the longest.
The climax of episode XVIII, "Jack and the Ultra-robots", when Jack doesn't retreat when his powered gauntlet runs out of juice, but kneels and prays to the gods that made his sword as the last robot approaches and raises its sword. Then, the true power of Jack's legendary sword is unleashed by the gods' response of divine intervention, and Jack cuts the robot in two in a single blow. "Unbelievable."
The "battle" between Jack and the "Tree Blind Mice" who are actually archers.
The archers get one as well in the beginning of the episode, wiping out an entire army of robots single-handedly.
And at the end of the episode, when Jack learns what the well did to the three men who wished to become stronger, he gets mad.
"Evil spirit of the well! You will not claim another innocent! I wish thee... DESTROYED!"
Jack's inner-fight with the darkness infecting his soul at the climax of "The Aku Infection". When all seems lost and Jack is slowly being swallowed up by the evil, the voices of his mother and father remind him of his accomplishments against Aku and the friends he has made in the future, building his will until he becomes a master samurai of light within his heart and vanquishes the evil of Aku from within. It is all just pure brilliance and a tear jerker for some.
Definite CMOH when they show the panorama of all those he helped throughout the course of the show (even in side episodes). You know that every single one of them is silently wishing for Jack to prevail.
The climax of the episode "Jack and the Swamp Monster". The episode appears to be going in the same direction as "Jack and the Warrior Woman", with Jack oblivious to Aku's Paper-Thin Disguise and going along with whatever scheme Aku has up his sleeve. Jack then goes on to sabotage Aku's plot at the crucial moment, revealing that he knew all along and was just waiting to strike, and a Curbstomp Battle ensues before Aku eventually flees. And surprisingly enough, the episode ends with Jack still in possession of the still-functional MacGuffin of the week.
The dramatic shift in power during the graveyard episode when Aku nearly kills Jack with his own sword. After the reveal that Jack's sword won't hurt the innocent, Jack gives a badass boast.
Aku: [After he loses the sword to Jack when it fails to kill him] How?! HOW?!
Jack: Even I had forgotten that the sword was forged in purity and strength. It can only be used for good. In the hands of evil it could never harm an innocent! And so, Aku, it cannot harm me... but it can harm you!
In a different way, Aku shows just how many different powers he has over one episode.
Not to mention the sheer tenaciousness with which Jack fends off Aku's attempts to kill him after losing his sword are quite the sight to behold.
Jack and the Creature. The Creature is a Totoro-looking teddy bear with intelligence inversely proportional to its size. It follows Jack around, destroying the time-travel-artifact of the week, and still follows an ever-more exasperated Jack. Then when a bunch of bounty hunters incapacitate Jack, it goes completely apeshit, transforming into a giant raging murderbeast Chuck and Ganondorf would be jealous of, and slaughtering the hunters.
Jack defeats a gigantic (700 ton) sumo wrestler by tickling him.
Pretty much the whole fight in 'Jack vs. Aku', easily topped by how Jack manages to drive Aku into having a panic attack with his genius gambit. Let me repeat that: Jack manages to drive Aku into a near blind PANIC. The smug look on Jack's face and his swagger as Aku was panicking is the icing on the cake. He may not have vanquished Aku in that episode, but he most certainly overwhelmingly won that day.
"Do you give up? Will you abandon their hope? Can you not feel their desperation? Will evil forever rule the world? HAVE YOU FORGOTTEN?!" All from three characters that barely even spoke during the episode.
The entirety of "Jack, The Monks, and The Ancient Master's Son." Kung-fu at its finest, ladies and gentlemen. Extra credit goes to the creators from using an incredible number of martial arts styles in this episode, from Tai-Chi and Wing Chun, to Eagle Claw and Southern Fist. Hell, they even included Water Beetle!
Jack defeating Demongo. Just epic.
Watch that scene again then listen to the music as Jack walks away as if he just beat yet another of Aku's generic mercs.
Also, the results of how he defeated Demongo. Demongo's strength came from the multitude of warriors, all capable of giving Jack a run for his money, he had fought, defeated and absorbed... And Jack freed them all. He didn't just defeat one of Aku's best warriors, he increased by a thousand the number of capable warriors willing to oppose Aku and his domain.
"Jack and the Hunters" gives us the Imakandi, a group of four lion like hunters that are one of two enemies that Jack faces and loses against. In fact, Jack spends all but the final few minutes of the episode running away from them.
Though Jack himself certainly deserves credit. He gives the Imakandi such a difficult time chasing him, that by the time they finally succeed, they have so much respect for Jack that when Aku shows up to claim him, the Imakandi rescue Jack and set him free!
The Flashback Episode with Jack as a child in what could be considered Africa. I don't really remember what happened at the beginning but Jack's mentor and his village are captured by these evil men wielding better weapons than their Simple Staves with only Jack escaping. Jack is miserable for a while until you see he train with the enemy weapon giving you a glimpse of the man he will become. He goes to the evil mens village and frees his mentor and his people, who all use the sticks that made up their cage as weapons and destroy the evil men in their own home.
Special mention to Jack's mentor who Curb stomps the evil men's leader who tore through Jack's own commandeered weapon like it was paper.
The Emperor has a few in the second part of "The Birth of Evil":
In the first part he tried to fight Aku with normal weapons, and was crushed. For the rematch he shows up with a magic armour (that he created himself), a flying cloud and what would become Jack's sword... And wins;
He has defeated Aku, and has no apparent reason to think Aku will return, or that he won't be able to take on him if it happens. He immediately starts setting up Jack's training, just in case;
Oh, and the magic sword? It was forged from the strength of the Human Spirit and Human Righteousness... Taken from him. That's right: the one thing that can hurt and destroy Aku was forged from his soul.
"Jack and Mad Jack", the episode starting off has Jack going into a Bad-Guy Bar, and as he sits down, the bounty hunters bring up the price on Jack, and he prompted defeats them in a split second.
"Seasons" depicts the epic forging of a Cool Sword. Crystals, lava, icebergs, lightning, runes, trial by combat... you name it. This was all the buildup to a Shaggy Dog Story, but it was mighty impressive while it lasted.
The "Fall" segment where Jack pretends to drink from the poisoned well, and when the Mad Scientist who made the poison sneaks up to check on his victim, Jack turns around, and spits the poisoned water into the villains mouth! Said villain promptly withers into dead leaves and is blown apart by the wind.
The episode where Jack visits The Scotsman's village and sees a traditional competition where men test their strength by throwing heavy stones. Jack is unable to so much as lift even one stone. He turns to a competitor and politely asks "How many stones do you weigh?" The competitor answers "Twenty stones." Jack declares that this man is "a mighty fellow" and shakes his hand...then promptly throws him to the ground. You are not misreading this: Jack threw a guy who was twenty times heavier than the stone that Jack previously failed to lift. (That's assuming all the stones are of equal weight, but even if you don't, the guy was still several orders of magnitude heavier.)
This is actually even more badass than it sounds because while Jack doesnt have the raw strength his opponent has, he instead outsmarts the challenge, and uses a simple martial arts technique that turns an opponents weight against them, allowing him to toss the huge Mook.
Episode XVI: Jack is caught off guard, captured and enslaved for a gladiator sport known as the Dome of Doom, where captured slaves are effortlessly slaughtered by experienced challengers. Jack proceeds to spend the entire episode mopping the floor with every last one, swordless, before the arena boss sends the last seven champions to attack him in unison... but Jack decides he's had enough playing around, and dodges all their attacks and makes for the weapons wall where the organizers put up various weapons for the challengers to use, allowing Jack to get his sword back, effortlessly curbstomp all seven champions and force the arena boss to free the slaves, killing one of the slavers on the way out. Badass does not begin to describe it.
Six bounty hunters team up in hopes of bringing down Jack and split the considerable bounty. They end up combining their individual plans which all had some flaw that Jack would be able to exploit, and it seems like it could work... but Jack avoids every single attack as easily as he would have had they been attempted individually.