Hmm.. I'm picky when it comes to characters, surprisingly enough. I don't usually choose characters by their personalities. If I like a character, I like a character, not just for their personalities or labels and whatnot. But there are a few traits most of my favorite characters have in common. So this may or may not make any sense.
Girls: In a girl, I like them to be couragous but dignified. The types of girls I like in animes are ones like Risa Harada from DNAngel. I don't care if people call her self centered and whatever. She's aware that she's pretty and she's not afraid to flaunt it. Also, I love an anime girl that has an attitude and can stick up for herself. I admire that sort of courage. Usually the overly saccharin pushover types bug me to no end, also those 'Damsels in distress' (i.e. Sakura from CCS, Shizuka from Yugioh..) But if they're nice and polite and not TOO sweet I like them (i.e. Haruka from Pokemon) Tomboys bother me too =P
Guys: Now guys.. are tough. First off, I don't usually like main character types. Yeah, I know it's wierd, but I HATE the sort of character that always wins and has no depth. That's why I usually love the side characters. I love a character that can be kind, humble, generous, caring, tough, smart, deep, tragic, or whatever. I just don't really like stereotypical stars. Ed from FMA isn't stereotypical, and neither is Naruto, that's the kind of star I like. Other then that, there's really no " I like this type of guy".
Both: All in all, I like a respectable character. If they're loud, rude, obnoxious, whiney, cowardly, lazy.. nah, I won't like them, unless they're purposely that way or if they can redeem themselves somehow.
And that's pretty much it. Go ahead an disagree with me, I don't mind.. I know my view on characters is messed up sometimes. What I wrote might not have made any sense anyways 0__o So.. yeah ^.^U