It is widely known that there is a severe shortage of women in fantasy novels. Given Tolkien's strong influence on most of the archetypes of the fantasy genre, some people believe this to be largely his fault. But I'm here to point out some of the more influential lady-characters from the fantasy genre.
The White Witch (Narnia)
I'm not a Narnia fan (you'll have to talk to Cassy about that one) but I do know you don't mess with the White Witch. I'm fuzzy on the details, but she is one scary witch.
Eowyn (Lord of the Rings)
I know some people feel like they're getting beaten over the head with an apology for the lack of women in the series when Eowyn says "I am no man" on the battlefield, but I think she's pretty cool. (I don't know if that line is in the book... I haven't gotten further in the series than Tom Bombadil. What a plot-momentum-killer.)
Arya Stark and Daenarys Targaryen (Game of Thrones)
Actually, George R. R. Martin is a revolutionary in the world of writing women in fantasy. (In interviews, he has attributed this ability to "thinking of women as people." I love this guy.) There are a lot of tough chicks in GoT, but these two are the first ones that came to mind.
Hermione Granger (Harry Potter)
Hermione, as you know, is one of my favorite characters ever, female or otherwise. She's smart, she's brave, she's gorgeous, but she also acts like a real person. Sure, she's like "okay, let's take down the most evil, deadly wizard ever" but when she gets attacked by powerful people, she has the good sense to be afraid and have a little mini-panic moment (without totally losing her mind like that bimbo from Indiana Jones).
Who's your favorite fantasy female?