Mugen's got too much awesome to list it all but here are some of the highlights:
When promised sex with a hot ninja girl if he helps her (but doesn't get anyway) he defeats an entire room full of armed guardswhile unarmed and half-naked, and in the dub even shouts something like "I want my nookie!" What's more, Yatsuha, the ninja, ended up falling in love with him, and swore to herself that she would find him again someday (as her partner questioned her taste in men).
The fact that Mugen dies at least three times in the course of the series is utterly awesome. Every time, he passes into Nirai Kanai, the afterlife of the Ryukyuan religion. He then tells the Futuchi, basically the Japanese grim reapers, that he's not ready, at least once demanding that they return him to the living world. Yes. Mugen basically tells the Grim Reaper to bite off.
Mugen nearly drowns after a friend betrays him, and survives with barely enough strength to drag himself to shore. After Jin fills him in, he uses his sword as a cane to hobble up to two of the conspirators and kill one of them effortlessly (three strokes of his sword in as many seconds), leaving the other, his childhood friend Kohza (possibly the only person who ever cared about him, and vice-versa) to live the rest of her life alone. She begs him to kill her, but he keeps limping away. End episode.Wow. Accompanied by the Crowning Music of Awesome.
Context makes this even more awesome: Kohza and the conspirator Batman Gambit'd Jin into killing her brother, just so said conspirator would be the only one who knew the location of the treasure (which Mugen originally helped steal). Which means that after risking his life to steal the gold, Mugen gave up any chance of ever finding the treasure in order to take revenge on his former comrades.
The second fight scene with Mugen and Sara. His opponent has truly awesome moves (like a lance that cuts the rain) and could easily have killed Mugen but she threw the fight when she realized her government handlers had killed her son long ago. The last scene ties it all together.
Let's not forget how Mugen deals with Umanosuke, the assassin with the scythe on a chain: Mugen gets really close to him, and after he throws his sword into the ground behind the guy, Mugen avoids Umanosuke's sword, bites his crotch, and then combines his sword, sheath, and his own body to catch the chain and boomerang it back to behead Umanosuke. It may be the first time in the series he's really thought about strategy.
Jin's got his own track record of awesome.
His final battle against Kariya Kagetoki, in which he deliberately allows himself to be impaled, which bring Kariya in close enough for Jin to draw his wakizashi and stab him back. He is also shirtless with his long hair down throughout the scene, which, according to the fangirls, helps. It also helps that he's using the Ultimate Technique of his dojo exactly the way it was intended.
Jin's fights with Yukimaru are also crowningly awesome. The first one ends with him leaping off a waterfall because he's reluctant to kill an old friend — Yukimaru is the only opponent he's ever tried to talk down. Their second meeting ends in Yukimaru's death with only the slightest movement of Jin's sword.
Jin effortlessly trouncing at least six sword-wielding thugs unarmed is pretty awesome. And made better by the fact that he's doing it to free an enslaved prostitute he's fallen in love with, even though he knows he's unlikely to ever see her again.
While it's also a Tear Jerker, the skill involved when Jin kills Master Mariya in self defense is truly impressive. He's asleep when the assassin enters the room but wakes immediately and it's over in less than 10 seconds. AND THAT WAS THE MAN WHO TAUGHT HIM.
Mugen and Jin enter a brothel, only to find one attractive prostitute (the above-mentioned Yatsuha) and a bunch of homely ones. Mugen beats Jin at rock-paper-scissors for the pretty one, leading to the adventures cited above. Jin, meanwhile, is later seen cutting down five men with one slash... and then collapsing with back pain as one of the prostitutes moans, "Oh, Jin..." Jin: capable of satisfying multiple women while still having the energy to wipe out several men in one blow.
Kariya Kagetoki may be a villain but his first fight with Mugen and Jin is still unbelievably awesome. Significant challengers to either have been extremely rare, but even when they team up to fight Kagetoki, they turn out to be hopelessly outclassed.
You people! What about Fuu?
"Her Stomach is like a cosmos unto itself." (Please note the capital letter 'S' when describing 'Stomach'.)
Her encounter with the various pots she bumps into in the fourth episode eventually leads up to some of the most impressive... uh, dicemanship, ever witnessed. The stunt even draws fourth a genuine (if momentary) expression of astonishment from the resident stoic.
Or the fact that she manages to keep the two men from shredding each other for the majority of the series?
Or even the very reason that she makes the entire journey with two virtual strangers just so she could find her father and 'slug him one' on her dead mother's behalf?
Plus she lied about that coin flip.
Several characters in the series (including Jin's Evil Counterpart and Jin himself) even comment on just how feisty and determined she really is. In fact, Samurai Champloo would be non-existent as a series if it wasn't for her!
Not to mention she provides the only recap episode ever that was worth watching.