Soul Eater is reasonably gender-balanced. The main main characters are a male-female weapon/wielder duo, the other main characters are considerably less flattering versions of the same (male wielders who should be competent but often aren't due to crippling mental quirks, straightwoman female weapons), and then the supporting cast is mostly male and the villain cast is mostly female.
Cowboy Bebop would probably count. It's a bit harder to say for certain on that one, because everyone did things
differently and counting Ed as female is debatable, but strictly speaking the main cast was split 3/2 (yes I'm counting Ein; he was confirmed male, right?) and generally all equally important/effective/well-developed.
Samurai Champloo might count, depending on how you define things. Obviously Fuu was never even remotely as competent at most things as the two male characters, but she was still important and interesting without just being a macguffin or useless side character who's there for no reason.
From western media, Avatar: The Last Airbender is pretty gender balanced. Sokka's a bit on the useless side most of the time, but I'd say he manages to be competent often enough to not just be a useless gag character, and [slight spoiler] joined in pretty soon anyway.
Hrm? I've never had any trouble relating to female characters. Or black characters. Or alien ones that are purple and of a weird third gender. All I need for that is for them to have human personalities.
I guess I'd agree with this, but "human personalities" might be a misnomer. Usually I end up rooting for whatever's cackling maniacally while doing horrible horrible things. :I