I love Buffy The Vampire Slayer. I'm a little too old for "fandom" in all its weird Internet forms, but I love Buffy. The "vampires, and the woman who slays/fucks them" (or in Twilight's case: "vampires, and the woman who stands around not doing much") genre is well-worn, but Buffy brought something new--agonizing emotional realism. The joy and pain of Buffy is that it's not a show where killing the bad guy makes it all okay. The heroes are in way over their heads just going through the normal transitions of adolescent life and dealing with the frictions within their own side; supernatural monsters are often the least of their worries. The fact that Buffy's much older boyfriend who breaks her heart when he turns ugly after they have sex is also a vampire is nearly irrelevant.
So is Buffy feminist? Oh yes, of course. But not for the obvious reasons. A physically strong female hero is nothing new and often crops up in utterly Neandersexual drivel. (Joss Whedon's tendency to depict waifish girls kicking ass has given me the same worry I have about Randall Munroe's tendency to draw female scientists--at first I thought it was feminist, now I think it might just be his fetish.) There's more than that separating Buffy from Lara Croft and Anita Blake.
Often, the vampire-fucking genre is used as code for the whole "women want bad boys" thing. In Buffy there's some of that, but more often it seems like she sleeps with vampires (especially Spike) because they're the only men who understand her life. Even if she could tell other men about it, they still wouldn't share in the underground, embattled world where she spends much of her time. In other words, she doesn't fuck vampires because women like that sort of thing, but because she does.
Maybe the most feminist thing about Buffy is the near-total lack of a male gaze. Buffy, Willow, and Anya are all very attractive, but they are never ogled. Their clothes are casual and practical, and the camera doesn't linger on their bodies. There's no particular effort at modesty, but you know how when many shows introduce a particularly good-looking female character, there'll be a little "va va voom, fellas" shot, a sweep up her body or a shot of her flipping her hair in that apparently irresistible way? Buffy doesn't go for that shit. Not that Buffy et al. aren't sexy, but they're sexy in that unconscious way that men on TV so often are. They're sexy while they go about their lives, rather than stopping to be sexy at the camera.
The feminism in Buffy also comes off as somewhat unconscious (although listen to Joss Whedon talk, and it's clearly not). Buffy doesn't see herself as a champion of women but of Sunnydale. There aren't any strawman sexists telling her she's just a girl. She's not prickly toward men in the way overt "feminist heroes" sometimes are and she (and the show) never rejects or resents the help of strong men. Buffy isn't out to prove she's as good as any man, she's just out to be the best she can be.
What I like best about Buffy is the strong and real personalities of all the main characters. You watch a few episodes (or, okay, all of them in a marathon can't-sleep-can't-eat spree) and you know how Buffy thinks and what sort of person she is. She's no paragon, she's not perfectly rational and she's not unfalteringly strong--but she's a person. She's not "a girl", not "a woman", not "a heroine." She doesn't exist to titillate or educate or symbolize. She's Buffy Summers.
That's feminism for ya.