I'm not one to pick favorite characters, or really even have strong opinions on characters, but KH is something of an exception because I can definitively say I have a favorite... but just one. No one else even comes close.
First, a couple of honorable mentions.
Terra. His story really could have been great, and relatable for me, but BbS did not (in my opinion) really portray him as going down this tragic, dark path. It was more that he was the victim of bad communication and the machinations of an old creep who wanted a new body. He doesn't even do anything that sticks out to me as morally questionable- the whole thing with Aurora's heart wasn't even him. Why do I have him as an honorable mention? Well... the friend who I roleplay with wrote Terra to be pretty endearing. I guess you could say that it's more the idea of Terra I've warmed to rather than the actual character in the games.
Xehanort (DR version). I briefly mentioned this one in another thread. Mostly, he's an honorable mention because of how he's written, at least in the three episodes of DR that we have. What really got me was the bit in chapter 3 when he's in the dark corridor, being blasted by these dark feelings, and then he says something to the effect of, "These reminded me that I could still feel." That line hit me like a ton of bricks. I've been through a pretty deep depressive episode, and honestly? Sometimes, during that period, there would be painful things that happened, and despite that, I welcomed them, simply because they showed me I could still feel. Looking back, DR Xehanort has some other moments where he's pretty clearly depressed. Basically, he's relatable to me in that way, and I like that because it's not something I come across all that often in media.
So who's my actual favorite? Well...
Xemnas. This one's a little complicated. Long story short, it's a combination of relating to and liking the character as written, as well as personal interpretation and experiences.
Going into more detail... My introduction to the series was Days. Xemnas didn't appear very often in that game, so I honestly didn't have much to go on, but I was fascinated every time he was around. It was like a special event- hey, the leader's on screen! I liked his design and especially liked his voice- I've joked to a friend that the guy could read the phone book and I'd be riveted. I liked the air of mystery (heightened by the fact that his appearances in Days were so rare), his vocabulary, and his intellect. I liked his weapons (I was and still am a fan of Star Wars, though really only the pre-Disney stuff) and hold the opinion that they're the most practical in the series (though who cares about weapon practicality in a fantasy world?). What really sold me on the character was how I was able to interpret him, though.
Like I said, Days was my first KH game, and for several years it was my only KH game- I was aware that KH was a series, but didn't know what happened in the other games and couldn't play them. I had also somehow failed to see that the Organization were supposed to be the bad guys (well, aside from the traitors at Castle Oblivion, though that was more because I was an Organization loyalist at that point). I had gotten Days as I was starting to spiral into the deep depression mentioned above, and so the Nobodies were relatable to me. Depression made me feel like I had no heart, and every time I was supposed to feel something, it felt like I was just going through the motions, so... with the Organization, I felt less alone in that regard. That didn't mean I liked them all. Days is RAX's story, and I... couldn't get into it. I gave up on story mode fairly early on and switched to mission mode to see if I could find somebody I could care about (I was fortunate enough to have a secondhand copy with a completed save file, so basically all missions were available). It took me a bit before I decided to try playing as Xemnas. And what do you know? I ended up caring. I actually played better (to be honest I've never been the greatest gamer), being strategic instead of just button-mashing like I did on story mode. I started constructing a clearer image of him, too- one that I really related to. He was isolated by his position as leader, just as I was isolated by depression. He was in a struggle for legitimate existence, which is something I felt like I was experiencing, too. I saw someone who was capable of both good and bad, but wasn't sure which direction to take- which again, I related to. He was someone who put on a mask when around other people, but who was actually deeply vulnerable and only showed that when he was alone- I was probably projecting at that point. And as I slid deeper into my depression, doing missions as him was really the only thing that kept me anchored.
Later I would experience other entries in the series, where I'd find out that the Organization were the bad guys, Xemnas was a version of this Xehanort guy and actually is super evil, and then there was all the convoluted stuff that DDD threw into the mix. That version of him is at odds with the one that I constructed. I've lost investment in the series partly because of that. That, and the fact that he's dead now... unless they bring him back (which on one hand sure, but on the other, it better not be just to kill him off a third time). I really feel like he got the short end of the stick in a lot of ways (I'm open to being wrong on this; I'm just voicing what my experience has been)- he's sandwiched between Ansem SoD who a lot of people remember because of nostalgia, and Master Xehanort who's the big baddie of the whole series Dark Seeker Saga. Xemnas is the middle child, maybe not forgotten, but less visible- kind of an appropriate fate for a Nobody, now that I think about it. I honestly wish he'd gotten more exploration- there were so many hints thrown out there (particularly bits that indicated a connection to TAV) that could have been so interesting but nothing was done with them. Still, none of that can take away the experience I had with this character, and he's always going to be my favorite.
Sorry for the essay. It's a long story and I tried (and obviously failed) to keep it short. I suppose it makes up for not having nine other favorites to list off... maybe?