Personally, I don't care if the character is male or female as long as they can stand on their own two feet and feel like they could be actual people making their own personal decisions. So like in the right hands and right execution, a female character who is the embodiment of femininity and the stereotypical housewife can still be three-dimensional, likewise so can a staunch feminazi or butch lesbian without hitting the audience over the head with it. (Because what works for the character in their story doesn't necessarily mean they can be the same in a different one. That doesn't mean they're badly-written, it just means their character/personality can't be the same to work just as well, so they end up turning into someone else entirely.)
Whether you agree or not (especially these days), Hermione Granger is someone I would consider to be a fleshed out female character. I mean, think about it: Could you describe who she is as a person if she were to exist, both the good and the bad side of her? And could you see how she progresses as a person (character) especially since you see her first as an eleven-year-old growing into a young woman? I can't think of too many female characters in the same boat as she, especially someone who got to grow up. There's a reason she was quite the role model for young girls growing up with the books/movies. 'Course, could she work as Hermione Granger in someplace outside of Harry Potter? Maybe, maybe not, but if I had to venture a guess, I'd say she could work well in many different environments.
Outside of literature and on the flip side of the coin, I like to look towards the character Nagisa Furukawa from CLANNAD as well-written. Again, she's someone whom you could legitimately see exist in real life, or maybe even know personally. She's weak in stature and rather meek, but on the inside once you got to know her, she is brave, wise, determined (or stubborn), and a little quirky (her whole family's like that), she's just not one to show it off. Those hidden depths were revealed because she was given a small push in the right direction when she needed it most--which was in the beginning of the story, but it's still a steady progression. Strangely enough, though, she works better as a character thanks to the main male character, but even he gets better as a character thanks to her. They're both characters who can stand on their own, but they work very well off of each other and help each other grow, which isn't too unusual in romances, but it does stand out.