Though it's a classic, so may have already been read by most here, I'll start by recommending Jane Eyre by Charlotte Brontë.

Genre - generally listed as some combination of Gothic/Romance/drama

Katniss from the Hunter Games is very strong in my mind

Okay, it may sound corny, but... Peter Pan? Wendy isn't exactly an ass-kicker, but she's a strong girl if you ask me.

Maximum Ride. The series starts getting ruined around the 4th book but gets OK again.

And, of course, The Hunger Games.

The Raging Quiet is a novel by Sherryl Jordan. It takes place in medieval times, when God was cherished and witches were burned. The novel revolves around a beautiful, hardworking young women named Marnie, who is sent off to be married to a lord in order to let her family keep their house and farm. Traveling to their new seaside cottage home with her new husband, she encounters a boy her age who is being whipped. Raver is known as a madman with demons. As fate turns, Marnie becomes his closest friend, discovering that his behaviour has nothing to do with madness. What Marnie doesn't soon know is that the villagers see her as a murderer and a witch. This is a novel of longing, and the danger of being different.

Also check out her other books: The Secret Sacrament and The Time Of the Eagle (two wonderful books with both equal strong female and male leads) :)

Retrieved from "http://en.wikipedia.org/wiki/The__Ra­gin­g_Q­uie­t&q­uot­;

Author Kim Wilkins: Gina Champion mystery series for young adults (2000–2006....its about a girl who has innate psyhic abilities who uses them to solve mysteries and also discover herself and her path in life)
Bloodlace (2001)
Fireheart (2002)
Moonstorm (2003)
Witchsong (2005)
Nightshade

Cate Tiernan: Wicca Series which follows the Wiccan adventures of a cast of high school students.
Book of Shadows
The Coven
Blood Witch
Dark Magick
Awakening
Spellbound
The Calling
Changeling
Strife
Seeker
Origins
Eclipse
Reckoning
Full Circle
Night's Child

His Dark Materials Trilogy - Philip Pullman
- Northern Lights
- The Subtle Knife
- The Amber Spyglass

The Mediator Series - Meg Cabot

The Millennium Trilogy - Steig Larsson
- The Girl with the Dragon Tattoo
- The Girl who Played with Fire
- The Girl who Kicked the Hornets' Nest

A Thousand Splendid Suns - Khaled Hosseini

North and South - Elizabeth Gaskell
(^ the miniseries is also a pretty good watch)

Hunger Games
Twilight Saga
Harry Potter (though I think we've read them all)

Well there's a series Gregor the overlander all the female characters where strong save to one cuz she doesn't and the other one cuz she's 2 LOL

I love the Samurai Girl Series by Carrie Asai. it has lots of martial arts in it (which i looove) and the main character, though annoying at times, is pretty kickass.
I agree that His Dark Materials is a wonderful series. Definitely read it!
And I HIGHLY recommend The Eight and The Fire by Katherine Neville. It has a very strong female lead (though 2 separate ones, mother and daughter) and the story is fascinating - it puts an interesting spin on history and teaches you about history and chess at the same time. And, of course, there's romance :)

Anita Blake Series by Laurell K Hamilton. Vampire hunter with a sense of humor.

Tamora Pierce is really good at writing strong female characters. I recommend starting with the Song of The Lioness quartet.

(Contains minor spoilers)

-The Skulduggery Pleasant series, a nonuplet set of books starring Valkyrie Cain/Stephanie Edgly (You'll find out why she has two names in the novels), and her growth as a person. She's a female ass kicker (in my oppinion) because she can fend for herself and doesn't obsess over the leading male like you'd expect characters like her to. She's really fiesty, sharp-witted and funny! It also features tanith Low who is a bad-ass warrior, and a feminist.
By: Derek Landy.
Genre: Crime and mystery/fantasy with a hint of dark comedy.
Age and gender range: Unisex book for 9+ year olds (yeah, it's pretty universal, adults, kids and teens are going mad for it.)
Fanspot: http://www.fanpop.com/spots/skulduggeryy-p­lea­san­t

- The demonata. Has some minor disagreeable traits (Most female characters are very promiscuous and scantily clad, like Juni Swan and Meera Flame. It also features Juni trying to escape defeat by offering herself up to Grubbs Grady as some kind of sex slave. O.o WTF moment: "I could be any woman you wanted...",), but on the whole features both girls and boys kicking some good ole' fashion ass. Bec Macconn (female lead in book 4 and 7, featured in book 6, 7, 8, 9 and 10) is the entire brains of the 10 books, often outwitting her male colleges and in the end was responsible for (spoiler) saving the world. Seriously, she owns it. She grew up in a time and place where a female's place was in the kitchen and she rebeled and defied sexist traditions. She was epic.
By: Darren Shan.
Genre: Horror.
Age/gender prefrence: Typically boys, but I'm a girl and i enjoyed it to some extent. Ages 12-15 i think.
Fanspot: http://www.fanpop.com/spots/the-demonatta-­ser­ies

Dearly, Departed. It's fairly recent, but it's a good read. Nora Dearly definitely holds her own.