Um.
Good question - especially because he hits a whole lot of my narrative hot buttons. :D So I've been trying to work out, exactly, what it is about him* that I like. (and ended up with a hell of a lot of digressions into heroes and anti-heroes, but hey. XD) I can't say why other people like him - I'm afraid a lot of it boils down to "He's cute!" judging by reactions to other bad guy characters I see online - but I can attempt to explain why I like him as a character.
* Which I need to do anyway, because the guy in the 'fragments of a dream' thing shares a lot of these traits and it's going to be bloody hard to write so that people understand the attraction. I think I also need to reread Louise Cooper's Time Master trilogy - I last read it when I was 15 or 16 and ISTR a lot of the same buttons being hit there also. I'm sort of afraid of doing that, though, because I may discover that it actually sucks. XD
[Warning: below this may be spoilers about character and motivation in Bleach, both in the Soul Society and post-Soul Society arcs, later volumes of Samurai Deeper Kyo a wee bit about Kyo, and a bit of Death Note, for L and Mello.]
First off: I love me a good bad guy. The hell with noble heroes: the bad guys, if they're not one-dimensional, are usually way more interesting, especially when compared to your usual shounen-retard manga hero. If they're the protagonist of the story, they're anti-heroes. Kyo in Samurai Deeper Kyo (at least as far as I've read - vol 24) lives here: he's bad-ass, not fighting for Good or Right or Protecting My Loved Ones (at least not overtly), he's out for his own goals and pretends not to give a damn for anyone in his way. Any hero who overtly fights to protect someone tends to give me the willies, because I'd prefer someone who fights beside me, or who pushes me to fight my own battles. This is why I've grown to really like Kyo as his methods and motivations become clearer, because he protects people by booting them in the butt to force them to become stronger, and why I like Kenpachi, too: Kenpachi protects Yachiru by making sure she's stronger than the enemy, not by wrapping her in cotton wool the way that Ichigo and the Karakura people do to Orihime. (I at least admire Rukia for taking Orihime and giving her some training, although she can't get her up to the level of the others in the time she has.)
Manji in Blade of the Immortal is like this, too: he's been, technically, a bad guy (in a world where there *are* no good or bad guys, really) and still sort of is. He helps and rescues Rin when she needs it, but at the same time helps her to become stronger herself.
So I like characters who aren't noble, and who don't run around trying to protect people. I *think* it's canon that Byakuya has pulled strings to keep Rukia from being assigned a seated officer position in order to keep her safe, which DRIVES ME UP THE FUCKING WALL (if it's fanon and not canon, it's certainly within his character), not to mention his tendency to keep people in the dark regarding his motivations, even when they REALLY FUCKING NEED TO KNOW. I already have serious ethical problems with him because of his rigid adherence to the letter of the law because of his vow when it doesn't occur to him that if the law itself is criminal, he has a moral and ethical obligation to attempt to change it, instead of submitting to it. (I draw a parallel here with criminal military orders: a subordinate has a duty to disobey criminal orders, no matter the personal cost. This topic is not explored near enough in manga, I think. :D) One of the signs of a good manga is that you have room to seriously over-think things in what is, essentially, a stupid shounen series. XD
I have *no* idea what fangirls see in Byakuya. I think he's reprehensible. I'd call him a snake except that I rather like snakes. Hell, I'd pick Gin over him simply because Gin *knows* he's an utter bastard and doesn't try to hide it behind a coat of honor. Byakuya's not tragic, he's a bloody idiot. This is also why I want to bitchslap Tousen: Tousen is Byakuya taken even farther in his rigid adherence to a personal moral code despite the costs to anyone and everyone else.
Second: intelligence. Ichigo and Renji and all of them are OK on some levels, but have the emotional and intellectual intelligence of a bag of hammers. I like characters with whom it seems I could have long, twisty, strange conversations and insights. Obviously, this would be where Kenpachi falls down. XD Gin, OTOH, is certainly intelligent enough to be able to work out what buttons to push to manipulate people, and my interpretation of him is that he's pretty damn smart. Kubo Tite may make him more cunning than smart in future episodes, but until that point, my interpretation stands. :D
Third: mystery. His motivations remain mysterious. It's possible that we already know his motivations, that he's simply a yes-man who attaches himself to the most likely-looking victor, but it's also possible that he's got motivations underneath that. We don't know. He lives behind the smiling mask, but when it's taken off, there's another smiling mask underneath it. Aizen falls down as an intriguing bad guy for me, because he's all "I wanna be a god MUAHAHAHAHAHHAAAA!!!!!" and there's no indication as to why, other than power-lust. (Gin is all "I'm just a total bastard," which I can understand far more than power-lust. XD) Anyway: we don't know what he wants or why he wants it. Aizen is a one-note bad guy who's pretty tiresome, actually. Momo's Stockholm Syndrome is the most interesting thing about him.
So - there's something about a man in a mask - it makes me want to find out what's behind it, and what makes him tick. If it's revealed too soon, or too early, then it loses its power. Sometimes, if it's revealed at all, it loses its power, which is why I rather like that Gin's mask still there - I'm not sure that knowing his true motivations would make him more interesting. (Although I admit the motivation of "Well, I'm just kind of a bastard" is way more interesting than power-lust, because it's not used that often in three-dimensional characters.)
In Death Note, L remained somewhat mysterious, because we never really learned about his childhood and reasons for his motivations, even as his character was slowly revealed. Mello - who is similar to Gin in his amorality (see #4 below) - retained my interest even though his motivations were transparent, because he was just fucking crazy and didn't have any serious high-minded motivation, which is awesome when it's handled well. But the high intelligence was a really good selling point; someone less so wouldn't have held my interest, I think.
Fourth: depth and amorality. The point at which Gin became my current favorite villain is the point at which he turned to Rangiku when she was holding him captive, and said something on the order of "It would have been nice to be captured for a while longer," and we see the flashback of when they were kids and he saved her life, and they stayed together. He's got depths there - he's not just the manipulative bastard yes-man, and he's not pure evil (although I read a fic this weekend that posited he said that precisely because he was evil - it was a good story and great logic, although not *my* interpretation of Gin, because a purely-evil person isn't as interesting to me as one with spots).
Note that L and Mello are also amoral, in a bit of a Machiavellian way: for L, the greater good is worth most of the techniques he uses to get there, although he does get challenged. Mello is the same way, although for "greater good," read "his personal goals." But their quirks and social maladjustment lead to their depth, or illusion of depth.
Fifth: But the Gin/Ran scene leads into the fifth point: the romance kink/cool bit of The Love of a Dangerous Man. This is not Reforming the Bad Boy, because there's no reform involved - it's more like being the only one who is safe from the danger (I see it as the clownfish who lives in the anemone's tentacles, safe from the venom, actually). We know he's capable of that, because of the Rangiku moment. This point is just a personal romance/literary kink, and if someone doesn't have it, they don't have it. I haven't run across it much in my non-romance prose reading: the Time Master Trilogy I pointed out in the footnote above had a bit of it, and I think Anne Bishop's gawdawful Black Jewels trilogy attempted to do it, before the Mary Sue emasculated all of the male characters and most of the female ones (when the Man is no longer Dangerous, he totally loses all his cool XD). It's what made Lord Byron so attractive, even though the guy was basically a complete jerk. I wouldn't characterize Gin as darkly Byronic in the least - although it's a standard romance trope - but he's still in the Dangerous Man category.
And the tricksy, shifting nature of him leads to interesting drama -
Sixth: as this is fiction, it allows for exploring this and other ethical dilemmas involved in unpredictable relationships safely. In real life would I go for a Gin? Hell, no: he's scary, sadistic, and unpredictable and I'd probably get PTSD or at least whiplash from all the about-faces if I were dating or even friends with a man like that. (Or, more likely, say "Fuck you! I don't need this shit!" and get the hell out.) But in fiction, you can handwave away, or ignore, the real-world consequences and the ethical dilemmas involved with unpredictability (as in the fic above) and violence: In Blade of the Immortal, I love Anotsu (and Manji, and Magatsu...) and would totally do him *within the context of his violent and amoral world*, but in real life there are very serious ethical issues with his actions. In Samurai Deeper Kyo, Kyo, also, is an intriguing and attractive character, but he lives in a fictional world of blood and pain and violence where you have to be the biggest, baddest motherfucker out there to survive and you have to spill a lot of blood to ensure the safety of the most number of people, and there are very, very few truly innocent civilians - he can be pretty sure that almost everyone he's killed deserves it. They're probably guilty of something, if not what he killed them for. If I were in that world, I'd totally do him. In this world: no fucking way. :)
Seventh: trickster archetype, which is a literary archetype I have liked for a really long time. There are several types of tricksters - the cheeky smartass that makes you want to slap him every so often (Bujold's Miles Vorkosigan, Bova's Sam Gunn, Ferris Bueller), the holy madman (*trying to come up with pop-culture examples and failing*), and the amoral shifty guy (maybe Mello fits here? Yukimura in Samurai Deeper Kyo might, also, but I don't know enough about him yet). There's probably a better name for that last subtype XD. (Coyote covers the whole spectrum there - he goes from almost evil, to a spiritual leader, to a smartass, to someone who ends up the butt of his own jokes; he's the One Size Fits All of tricksters.) Gin fits the last subtype - he's explicitly drawn to resemble the Japanese kitsune, with pointed features and slanty, slitty eyes, and his name kanji are a play on the phrase "silver fox". Foxes in Japanese (and Asian in general) folklore are almost never fully evil. They're tricksy and amoral and driven by whims, but not relentlessly evil. They play tricks because it amuses them, and may grant boons to or punish someone out of whimsy or personal revenge, and can be loyal friends and lovers or relentless enemies, sometimes at the same time,* which makes them far more interesting than pure good or pure evil archetypal characters. They're not out to rule the world, just tiny bits of it. I, especially because of my background in anthropology and my interest in folklore and Jungian archetypes**, can't help but interpret his character in this light.
* I've read several stories so far in Strange Tales from a Chinese Studio by Pu Songling that deal with fox lovers who have a genuine attachment to their lovers but who also, at the same time, are slowly killing their lovers because every time they sleep with them, they draw away part of their life essence, as Taoist thought has it.*** If they stay away for a few days in between sexual encounters, the lover-victim can regain the essence, but the love-bonds are strong enough that neither partner can resist, with sometimes fatal consequences. I think that sort of encapsulates the attitude towards foxes - occasionally the fox doesn't care they're killing their lover, but sometimes it's a source of great sadness to him or her that they can't resist their desires. (I think I may need to explore this in regards to the thing in my head: how can you make it convincing that someone wouldn't resist it, if they truly loved their partner? It would require an alien mindset, which is something else that I want to explore. Huh.)
** Probably goes with my librarian needs to categorize things. XD
*** One is even a gay relationship, which is quite interesting, and would make a good yaoi manga. Hot mansecks! Lovers killing each other even as they make love! Reincarnation! Godawful puns made possible in the English language since the characters are named Huang and Wang, which I keep reading as Hung and Wang! Suicide! Corrupt officials! Drugs! Bisexuality! Date rape! Crossdressing! Bad poetry! And all in ten pages!
So there you have it - lots of random thoughts on heroes and villains and what makes characters interesting for me. :D There's a lot more - I haven't even bothered to figure out why I love Hotaru in Samurai Deeper Kyo or to really examine the big bruiser with small wee cutie archetype that I like. Hopefully this will spur some interesting discussion in the comments, since what was supposed to be a short answer explaining a character's appeal turned into a Fucking Fandom Essay, just about.

Page 1 of 4