I would have said "don't care, it's all about the plot," but that's not really accurate to the way I approach stories, especially in regards to the lead character or main perspective. Rather, plot is just one element in the whole I consider really important. There are books I love where plot is somewhat less important than other elements.
Basically, I don't have a strong preference one way or the other. When I was younger, I might have said that I tended to read books with male protags and certainly most of my stories were about them. As I've gotten older and read more widely, that has been less the case, and I have tried to even out the field as far as female protags and writers go. I think even us women cave into ideas about what those things entail, and I do buy the idea in feminism that women often internalize the male gaze and general expectations of their gender.
I recall reading some research that said men tend to have a harder time related to female characters, whereas women tend to be more flexible. Personally, I don't think is innate but the way culture sets up the male perspective as "default" and the female perspective as "other."
Whatever works best. I just don't want to see a lady or a dude for the sake of being a lady or a dude. Same with everything else about them—if you want to write about a character who's disabled or a minority or whatever, make sure it's for a reason.
Hm. See, originally I was going to say, "I don't care," but then I started thinking about my favorite books, and most of them have male protagonists, even the ones written by women. So perhaps I'm subconsciously drawn to male voices because they're different from mine? Or because I'm heterosexual and thus find the male voice more attractive?
Or maybe it's a coincidence, because most of my favorite books are sci-fi, and that's traditionally a male-dominated genre.
I prefer female characters over male characters because from the tons of books i've read they tend to be written with more humor, which I like. Male character's tend to be rigid from everything i've read. But overall, if the plot if great I don't really mind.
I don't know if this is an issue you have when reading, but if a character is badly written but the plot is really good, I still hate the story. The story can be amazing, but if the character is lame, I can't handle it.
Gender's pretty irrelevant to me, so long as the character's well-developed. I mean, the attributes that make a character interesting aren't particularly specific to any gender - are they dynamic? mentally unstable? resourceful? clever? It's not really a boy or a girl thing. There's still probably some difference in perspective with a male author writing a male character vs. a female author writing a female character and vice versa, but considering dA regularly referred to me a as a dude in my first few features, it really doesn't seem to matter much.
I generally don't care in movies either, though I'll admit that lately I've been drawn to female directors with female protagonists - Catherine Breillat, Jane Campion, Julia Leigh, etc. - in large part because of how they handle sex and relationships in their films. But then again, part of that could also be that they're foreign, and the U.S. can be kind of weird about sex.