I notice, OP, that you mention games with customizable characters. I'll get to that in a quick second.
I like to play female characters, mostly in third-person games. My justification is that if I have to look at some schmuck's ass bouncing around on the screen for the entire game, it might as well be an ass I enjoy looking at. One important caveat is if the female character plays differently from the others, a la Borderlands, I will only pick her if I like her abilities/moveslist. When I play Tekken 5 I have a small stable of regular characters I call "The Band of Shirtlessness," and the only female on the list is Christy Montiero, because to my thinking that double-boob-sling thingamabob she wears would require a rather liberal definition of "shirt."
In games that involve fully customizable characters, not only do I have female characters, I have at least one female legacy character; that is, a character that shows up game after game after game. Her name is Elmo Orly, (because that's how I imagine "lmao" would sound if you said it out loud, and the last name is pronounced "ORR-lee") she typically has black or dark blue hair, black makeup, tomboyish attire, and as a personal joke she is characterized as being a lesbian, but because most games do an either terrible or nonexistent job of characterizing lesbians, she never meets anyone, and so she's constantly frustrated. She takes this out in combat, adopting the general "sneaky bastard" style of fighting to snipe, poison, or trap/ambush her targets. What made the whole "lesbian" thing even funnier was Fallout NV's "Cherchez la Femme" perk, which presumable makes your character a lesbian, and it still only comes up all of three times in dialogue!