It depends on the genre I'm watching or playing. When it comes to things like anime, I prefer "realistic" guys in harem anime (that is, one guy, lots of women) and not the doofy "I'm in heaven!" type guy. I like that guy to already know which of the potential romances he wants, and to act/react accordingly to the advances of the others and try to figure out how to win the heart of the one he does want. If we go into anything that's "combat" type anime, I prefer characters that are INTELLIGENT. As in... they think ahead, they've got a plan, they reason, they solve, and outwit their enemy. I don't like the standard, "Oh, I just have more power" or "I magically unlocked more power because plot demanded I do so" in order to win. That's boring. Probably why I find most Gundam anime to be horrifyingly boring. If we're talking comedy, I prefer a guy who is making the jokes to the one who is the butt of all the jokes. If it's "slice of life", I prefer someone who is simply charismatic (their flaws are their flaws, strengths their strengths, but I prefer them to just be a people person).
If it's a video game... I prefer basically anything that's not a "Mary Sue". Part of my problem with the new Lara Croft is how "Mary Sue" she is. She can do anything, without practice, without having ever done it before, and get herself out of tons of scrapes, and she knows every piece of lore about everything ever, and can fire guns with pinpoint accuracy and beat thousands of badguys, and never once accidently causes problems or gets people killed or is selfish or yells at people because she's frustrated in the heat of the moment... Mary Sue. Boring. No character. No depth. I want my characters in a video game to just not be Mary Sues. They should make mistakes. Their personalities should have downsides. Their actions should have real consequences. If they're funny, they should accidently tell a joke at an inappropriate time. If they're charismatic, they should accidently make friends with the wrong people. If they're smart, they should sometimes make a mistake that cannot be fixed. Etcetera, etcetera.
I don't really care about gender. You'll find most people don't. A hero is a hero is a hero. Even if that hero is sometimes a heroine. In fact, even if your hero is a girl... still a hero. No need to make the distinction that she's a heroine. A hero is a hero is a hero. I dislike whiny male characters as much as I dislike whiny female characters. I dislike Gary Stus as much as Mary Sues (though I file both under Mary Sue, since it's more universally recognized). Unless the gender of a character has a major bearing on the plot or situations of the movie, book, anime, video game, whatever... I don't think the gender matters in the slightest. Though, if you make a big deal in your game about your protagonist being male or female (namely being cliché and using stereotypes), I'm not really going to be interested.
People are people first. Write people. People are everything else secondary or tertiary. Most people don't think of themselves as personality traits or genders or whatever else. People think of themselves as people.
I like those kinds of characters. The kind that think of themselves as people. That think of the way they do things as the right way to do things. Or, the only way they can accept doing things, because they couldn't live with themselves if they did things a different way.
