Kyo himself, at times. He's vicious, rarely shows anything resembling empathy (especially near the beginning), and his kills can be brutal. But he's also a badass among badasses, and his Implausible Fencing Powers and impressive snark make him highly entertaining.
Shirogarasu was surprisingly popular and stayed in the top 10 in character polls for a long time, despite his short tenure as a character and very minor role in the overarching story. He was still 18th in the final poll... when he'd been dead and unmentioned for over 30 volumes.
Akari is beloved by the fandom, partially because she's one of the best-handled Transgender characters in manga history (even over a decade later!). She's incredibly badass, always portrayed as a woman, not a crossdressing man, and when there are jokes centering around the fact that she is trans, they are always at the expense of the Jerkass mocking her.
Fandom Berserk Button: The anime. Good god, the anime. To the point that most fans of the manga pretend it doesn't even exist, because it's such a departure from the source material that it's essentially SDK In-Name-Only. And because it only loosely followed the first sixteen volumes, two of the above Ensemble Darkhorses (Hishigi and Akari, who debuted in volumes 20 and 22 respectively) didn't even make it in. "SDK anime? What SDK anime?"
Harsher in Hindsight: Yuan refers to Hishigi as "an incredibly efficient executioner" when explaining why getting any information out of him is going to be difficult. We find out later that Hishigi has quite literally acted as the Former Crimson King's executioner, and he killed Yuan's mother on the king's orders.
Magnificent Bastard: The Former Crimson King, certainly. Yukimura also definitely qualifies, and Nobunaga might.
Specifically, Yukimura's tactical and strategic skills are such that Ieyasu would rather bribe him than have him as an enemy. At the end of the series, he successfully anticipates the Former Crimson King's plan and has already had Okuni rally together the combined forces of the Tokugawa, the Sanada, and the Date to contain the King's blood soldiers and keep them from rampaging out into the human world.
Shinrei was ridiculously adorable as a child. Sweet, idealistic, fluffy little prodigy. Knowing that he was abused and manipulated into believing the Mibu's A God Am I and Might Makes Right philosophies is heartbreaking and has triggered many protective instincts.
Moral Event Horizon: The Former Crimson King has reached it repeatedly. Every time it seems that he's crossed the horizon, he takes the evil further.
Before the events of the manga, he manipulated Kyoshiro (through Chinmei) into killing Sakuya's brother, and arranged for Sakuya to watch. Made worse since Nozomu was also Yuya's adoptive brother, and his death was her Cynicism Catalyst.
Muramasa lost all faith and abandoned the king after his We Have Reserves speech on not bothering to cure the Death Disease.
Fubuki is near death by the time Tokito finds him after regaining the memory that he is her father. She begs the Former Crimson King to save him, to which the king responds by trying to murder her. Fubuki (already dying and likely beyond saving) takes the fall, and the King complains that he was just trying to let Tokito die peacefully instead of fighting him and suffering.
Slow-Paced Beginning: The first few volumes read a bit like an attempt at cashing in on the popularity of Rurouni Kenshin. The beginning is still enjoyable, especially once SDK finds its own uniquely odd voice, but the narrative isn't anything mindblowing. The real plot with the Mibu hits in Volume 10, and from then on, we have something extraordinary on our hands.
They Changed It, Now It Sucks: Ho boy. Simply put, the anime adaptation is SDK In-Name-Only. It only shares a very small handful of similarities with the manga, and ended up very different in everything from art style to characterization (for example, beloved Cloudcuckoolander Hotaru is totally serious). It would have been difficult to make a good adaptation, considering the anime is only 26 episodes to the manga's 306 chapters and 38 volumes, but it doesn't change the fact that many people try to forget that the Animated Adaptation exists. It also didn't help that the anime was made in 2002, when the manga was less than halfway finished.
Too Cool to Live: Muramasa, Taihaku, Fubuki and Hishigi. One can also make an argument for Kyosaburo, who created the Mumyo Jinpu Ryu before passing it on to Muramasa, and therefore to Kyo by proxy.
Uncanny Valley: Kyo's Crimson Eyes look strange and intimidating, but they fit with his overall aesthetic and personality. The Former Crimson King's and Kyoshiro's variants just don't look right, and the Mibu Reconstruction Plan's child experiments are even worse.
The fully awakened eyes are downright scary.
Values Dissonance: One of the reasons Kyo reads so much like a Designated Hero is that he's presented as incredibly admirable despite being a giant dick. But in the context, being a badass is an admirable trait in and of itself, so it's a little easier to accept.
The Woobie: Tons of characters, notably Yukimura. Pretty much any character who gets any attention from Kamijyo has some Woobie elements.
Iron Woobie: Akira. Jaded street urchin, turned Tagalong Kid to Demon Eyes Kyo, turned Child Soldier (a willing and enthusiastic one, but still). Intentionally blinded himself to attain greater strength after Kyo disappeared. Worked harder than anyone in the entire story to get to his current level, then is told that it's physically impossible for him to get any stronger than he already is because he doesn't have samurai lineage. Finding a way to temporarily power up and defeat Tokito, but completely and permanently wrecking his body in the process. He never seems particularly upset or bitter about any of this, aside from a brief Heroic B.S.O.D. after Anthony tells him he can't get stronger.
Stoic Woobie: Hishigi, good god. He is in constant, excruciating pain from the Devil Eyes and the Death Disease. He has watched countless friends die horribly while he was helpless to save them. But he keeps fighting for Fubuki, because Fubuki is all he has left. And not once does he complain about any of this. He even tells Fubuki not to feel sorry for him while he's dying in Fubuki's arms, because Hishigi chose his own path and Fubuki is not allowed to blame himself.