Hoboy.... this is one of those things that's really hard to discuss with anyone, just because it often seems so freaking weird. This thread though, it makes me think that maybe this sort of thing is alot more common than I thought, at least among autistic types.
My central character obsession is Bridget from Guilty Gear. I'm not entirely sure what caused me to latch onto him originally as I did, but I found him shortly after trying the game for the first time, and then... well, everything changed. I try to be like him, I try to have an androgynous/girly appearance like he does (and in my case that's not particularly hard to do, fortunately for my sanity, despite that I'm male). I got into cosplay not long after finding him, and of course he was the main one I wanted to cosplay as. I even grew my hair out for this, it's very long now. Some of the attachment might be due to the fact that I seem to also kinda have gender issues.... and the cosplay lets me explore/express that a bit.... but really, I just love the heck outta the character, and feel the need to emulate him, and I try to capture all of that with the cosplay. He's also my best character in the game, and just overall (and I play alot of fighting games), I've got every figure of him that was made up to this point, I've got doujins, and other.... stuff.
He's my main obsession, a fact which hasnt changed at all, but there are other ones as well. I latched onto Noel Vermillion from Blazblue as well, another one that I do a cosplay of, and recently my third biggest character obsession randomly became Labrys from Persona 4 Arena; the funky thing about that is I'm not really even all that familiar with the Persona series beyond that particular game, but regardless, I just ended up really liking her alot. Will be doing a cosplay of her as well. I swear, the cosplay is the part that makes all this the most embarassing, since I'm NOT a girl. It doesnt even matter that people tend to think these look good when I do them, I still tend to be easily embarrassed and perpetually nervous when doing these. That aspect has been hard to deal with.
There are other character obsessions that I would classify as being smaller ones.... Ruiko Saten and Index (who both are from the same overall anime universe, though Ruiko is from a spinoff of Index's main series), Squid Girl is another one, Len from Vocaloid, Kurapika from Hunter x Hunter, Misery from Cave Story (thus my name and avatar on here) and there's a few more beyond that. They dont quite compare to those top 3, but they're still there, and they have an importance to me.
Ahh, it's good to get some of this out into a written form, really. I have a very hard time talking about this sort of thing with most people I know. A few of them know about it and understand it, but not many. I've always avoided talking about it and such because of the embarrassment factor and the "weird" factor. But it seems I'm not alone in this one, and that really does help.