This was painfully hard to whittle down to ten. Rest assured that the runner-up list is long. But I had to go with my heart.
Listed in order of when in life I first encountered them (as near as I could get it):
1) Karana from The Island of the Blue Dolphins by Scott O'Dell.
Here's a young female character who kicks ass in a situation that would be daunting to anyone: having to survive alone on a small island that you are sharing with a pack of wild dogs. I'd probably be eaten the first night; Karana builds a fence out of whale ribs to keep the dogs out. Having sacrificed herself to save her little brother only to endure the agony of losing him, Karana lives alone for many years, becoming ever tougher and more resourceful, until she's such a boss she is able to tame an injured wild dog and make it her beloved companion. I admired the hell out of her when I was a kid, and writing this now, I'm finding I still do.
2) Hermione Granger from the Harry Potter series by J.K. Rowling.
Such an obvious choice I worried it was too obvious, but decided I couldn't penalize 'Mione for being just that awesome. She's brilliant and ambitious and principled and driven, and in seven books never apologizes for being those things and a girl at the same time. She has the strength, skill, and bravery to face down all manner of magical peril, but also the moral courage to stand up for what she believes in when everyone else is rolling their eyes at her, to tell her best friends when they're being lazy or unkind or just plain wrong, and to fight oppression even when the oppressed are being racist jerks to her. She is amazing, and I wish I'd had the privilege of reading her when I was a young girl myself.
3) Katniss Everdeen from the Hunger Games Trilogy by Suzanne Collins.
Another obvious choice, and another I couldn't pass up. Katniss is the ultimate tough girl, holding her own in a televised fight to the death against twenty-three other teenagers, some of whom have been training for this event their whole lives. While the hot temper and ace archery skills are entertaining, what I love most about Katniss is how morally gray she is, and how she sees that she is morally gray. She is not the Good Guy of her own story; she sees her role as protecting the real Good Guys (her sister and some of her competitors), and she is willing to endure unimaginable horrors to keep them from physical and moral harm. All of which makes her another, more complicated kind of Good Guy.
4) Admiral Jane Roland and Ensign Emily Roland from the Temeraire series by Naomi Novik.
It's probably cheating to cite two different characters from a series when they are rarely on-page together, but since they are mother and daughter I'm giving it a pass. What I find so delightfully kick-ass about Jane and Emily is that they don't think they're extraordinary for being kick-ass women in the nineteenth century. Having both been raised in the subculture of the dragon pilots, they are in a way as ignorant of "normal" women as those women are of their existence. They don't know how disempowered they "should" be, and there is something amazingly refreshing about that. Neither is described as particularly attractive, yet both have fiery romantic relationships-- which take a firm back seat to the things that really matter, which are their military careers and their devotion to their dragons. They are bold and passionate, and entirely unconflicted about it. They are shining examples of how high women can fly if no one clips their wings.
5) Sadie Kane from the Kane Chronicles trilogy by Rick Riordan.
Sometimes kick-ass female characters can be a little intimidating. They have flaws, but often they're of the "she kicks a little too much ass" ilk. But Sadie Kane is a realistically flawed thirteen-year-old girl. She's impulsive and boy-crazy and self-aggrandizing and often unnecessarily rude. Unlike nearly every other character on this list, she cares a lot about what she looks like, and presents a carefully cultivated pop-punk image. Despite all this, she is kick-ass enough to host the kick-ass goddess Isis without being overwhelmed by her, and to describe it all with snarky, wonderfully British aplomb.
6) Peaceful Hortense Elaine Warren, aka Sister Peace, from the Castle Waiting graphic novels by Linda Medley.
A kick ass nun, y'all. Sister Peace is from an order of feminist nuns who all have beards, and, more importantly, strive to give everyone what they truly need. Peace is so funny and cool, and seems completely comfortable in her own skin-- beard and all. She's got guts to spare: the guts to run away from her tiny village and join the circus, the guts to save her best friend from a bad situation, the guts to resist becoming the abbess and wander the world instead, the guts to continually spar with (and defeat) a truly disturbing-looking demon, and the guts to devote herself to saving the souls of the residents of Castle Waiting-- but in such a low-key way they think she's just being a goofball.
7) Gratuity "Tip" Tucci from The True Meaning of Smekday by Adam Rex.
This twelve-year-old African-American girl in a slightly goofy alien invasion/buddy road movie Middle Grade novel written by a white man may be one of my top 3 characters of all time. She's brave and independent and hilarious and so, so smart, but what really gets me is her total honesty. She's honest about not having everything figured out, about being wrong sometimes, about her mom being kind of childlike, about the things that don't make sense in the world, about the racism she encounters, about her less-than-noble feelings. I adore her, I admire her, she makes me laugh, and she breaks my heart.
8) Flavia de Luce from the Flavia de Luce series by Alan Bradley.
Another twelve-year-old girl, this one a chemistry prodigy living in a rapidly declining manor house in post-WWII England and solving murders in her abundant free time (seriously, does she ever do any kind of schoolwork?). She's a bundle of contradictions: precocious yet naïve, aloof yet aching to belong, coldly dispassionate about the many corpses she encounters yet tenderly devoted to her father's traumatized manservant, constantly plotting to poison her older sisters yet longing for their love and acceptance. She's brave and resourceful and frighteningly intelligent, equal parts Sherlock Holmes, Pippi Longstocking, and Marie Curie, and steely English gentry to her core.
9) Senneth Brassenthwaite from the Twelve Houses series by Sharon Shinn.
Senneth is a Fantasy rarity: a romantic heroine who is neither young nor beautiful. She's a crazy-powerful fire mystic in her late thirties, and her natural badassery is tempered by the wisdom of age. She pretty much does as she pleases, but often what she pleases is helping other mystics, whether by rescuing them from bad situations, mentoring them in the use of their powers, or being sent by the King to investigate crimes and plots against them. She is the heart of the band of adventurers the series focuses on, the sun around which the others all revolve. Her romance with the gruff King's Rider assigned to protect her on her journeys (hilarious because she could literally roast him alive with her mind if she wanted to) is one of the most grown up love stories I've ever read. She's strong without being show-offy about it, and vulnerable without shame. She's a kick-ass adult.
10) Betty, Dee, Hannah, and Violet from the Rat Queens graphic novels, by Kurt Wiebe and various artists.
While I have tried on this list to embrace the many different ways female characters can kick ass, I had to include this quartet of female mercenaries who literally kick all the asses. I love it that for all the angsty back stories and complicated romantic entanglements and PhD's in Bad Mofology, this is really a story about sisterhood. When it comes down to it, nothing matters more to the Rat Queens than each other, and that's awesome and unexpectedly touching for a graphic novel with so much blood splatter.