Contrary to one definition presented in a WU for fanboy, fangirls not only exist, but are more common than you might think. Go to any shounen-ai or yaoi circle and you're bound to find a fair share of them. Not that such people are limited to slash; you can find fangirls of fantasy novels, Star Trek, and, yes, even Linux.
However, just like the stereotypes that the term "fanboy" brings to mind, fangirl isn't exactly a flattering term. I give you a rant that a friend of mine wrote on the topic, brought to you with her permission. It explains things more eloquently than I probably ever could.
There's this dichotomy going on, I think. Consider this. How many male fans of anime/manga/games do you know that call themselves "fanboys" in a public arena? I mean, imagine reading this on someone's profile page:
"My name is Bob. I'm 19 years old and a huge fanboy."
So if you read that, what do you envision? You probably start to think of an unwashed nerd with taped-together glasses, sitting in his parents' basement, unable to communicate with humans that exist beyond a computer screen except in a convention environment - at which he wears the same Sailor Mars t-shirt for the entire 60 hours that he's at the convention. If he talks at the convention, it'll be about Gundam specs or his favorite scene out of La Blue Girl. Without any knowledge of female anatomy or how it works, he writes fanfics about Sailor Moon getting it on with Sailor Jupiter. And he will hit on a Japanese girl just because she's Japanese, not because he cares about her for any other reason. Not too flattering, is it? And this image of a "fanboy" is broadcast everywhere, from parody videos to convention brochures to t-shirts. Is it any wonder why no self-respecting male fan calls himself a fanboy in public? With that kind of stereotype associated with the term, I can't imagine why anyone WOULD use "fanboy" to describe himself, even if he perfectly fits the stereotype. Are all male fans like this? No. Are all guys who like anime porn like this? ...uh, I dunno. But this is the stereotype.
However, this appears on countless profile pages:
"My name is Mary. I'm 19 years old and a huge fangirl."
In the same way that some female fans seem to think that yaoi == "artistic expression of tolerance and beauty" while hentai == "dirty, exploitative, horrible porn", fangirls seem to have this idea that the phrase "fangirl" does not have any negative images associated with it that the phrase "fanboy" does. Well, I believe that there ARE negative images associated with the phrase "fangirl". When I hear "fangirl", I think of someone who spends most of her time screaming and jumping up and down uncontrollably at the sight of two guys holding hands. She runs around shrieking at conventions, and tries to hump the legs of good-looking male cosplayers. And because so many self-described "fangirls" are yaoi fangirls, I think of a person who completely ignores canon in a series and immediately slashes any two good-looking guys in a series. Without any knowledge of male anatomy or how it works, she starts writing fics in which Heero and Duo have sex for hours. She doesn't care about the plot of a series, or whether or not it has interesting characters - what immediately attracts her to something is whether or not it has Gay in it. And she will worship a gay guy just because he is gay, not because he has any other redeeming qualities.
Are all female fans like this? No. Are all yaoi fans like this? No. But this is, IMO, the stereotypical fangirl. And I don't want to be associated with this stereotype. I've seen a lot of fangirls who fit this stereotype. And they don't get respect outside of their own circles. A lot of male fans hear "fangirl" and shrink away, because they expect to get accosted with a bunch of pictures of men screwing each other in the butt. And you ought to hear a certain gay male friend of mine talk about his experience with fangirls. ^^; For the record, there are a lot of fangirls who aren't yaoi fans, but the outspoken ones seem to be the yaoi fans. Fangirls are seen as unprofessional and immature, loud and annoying, and generally not the type of person you want to be seen in public with.
Am I a fan? Yes. Do I like anime and manga and games? Yes. Do I like the gay? Yes. But do I want to be considered on first impression to be a screaming adolescent who only cares about mansex? No. Which is why I don't like being introduced as a fangirl and why I don't label myself as a fangirl.