It's interesting, though I've read many, many books with female protagonists, my very favorites (LotR, The Thief, etc) do not. But here are a few (*cough cough* understatement) recommendations. 

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Realistic fiction (fairly modern day):

The Penderwicks (series) by Jean Birdsall

Historical fiction:

Some classic series: Little House on the Prairie, Anne of Green Gables, and Betsy-Tacy 

One Crazy Summer, by Rita Williams-Garcia (first in a series) 

Hattie Big Sky, by Kirby Larson 

Esperanza Rising, by Pam Munoz-Ryan 

Roll of Thunder, Hear My Cry, by Mildred D Taylor (part of a series)

Calico Captive, by Elizabeth George Speare 

Bat 6, by Virginia Euwer Wolff

The Fences Between Us, by Kirby Larson 

The True Confessions of Charlotte Doyle, by Avi  

Fantasy/sci fi: 

The Castle Glower series by Jessica Day George

Ella Enchanted by Gail Carson Levine

A Tale of Two Castles by Gail Carson Levine

The Wish, The Two Princesses of Bamarre, and Fairest, also by Gail Carson Levine 

A Wrinkle in Time, by Madeleine L'Engle (first in a series)

The Princess Academy, by Shannon Hale (series but I only like the first one)

The Treekeepers, by Susan McGee Britton

Dealing With Dragons, by Patricia C. Wrede (I think it's a series) 

Misc:

When You Reach Me, by Rebecca Stead 

Remarkable, by Lizzie K. Foley 

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That should get you started... 

So many great recommendations by all of you! Although I don't think anyone has mentioned two of my favorites, The Blue Sword and The Hero and the Crown by Robin McKinley :)

-Admin 

Thank you everyone for the wonderful recomendations! I'll have to get a few of these from the library. Thank you so much!

Here's some of my favorites! 

Fantasy and Adventure

The Apothecary by Malie Meloy

Theodosia and the Serpents Of Choas by R. L. LaFevers

The Wildwood Chronicles by Colin Meloy

Where The Mountain Meets the Moon by Grace Lin 

Emmy and The Incredible Shrinking Rat by Lynne Jonell

The Magic Half by Annie Barrows

The Glass Sentance by S.E. Grove 

The Name Of This Book Is Secret by Psuedonymous Boch 

The Incorrigible Children Of Ashton Place by Maryrose Wood

A Snicker Of Magic by Natalie Lloyd 

Nimona by Noelle Stevenson (graphic novel)

Lumberjanes (comics)

The Secret Of Zoom by Lynne Jonell 

The Secret Of Zoom by Lynne Jonell 

The Sister's Grimm by Michael Buckley 

Matilda By Roald Dahl

Remarkable by Lizzie K. Foley

The Luck Uglies by Paul Durham

The Wolves Of Willouby Chase 

The School for Good and Evil by Soman Chinani 

Historical Fiction 

Someone Named Eva by Joan M. Wolf 

Fly Girl by Sherri L. Smith 

Chains by Laurie Halse Anderson

The Dear America Books 

The Lions Of Little Rock by Kristin Levine

The Mighty Ms. Malone by Christopher Paul Curtis

Sophia's War by AVI

Red Scarf Girl by Ji-li Jiang

Number The Stars by Lois Lowry

A Little Princess by Frances Hogson Burnett 

Stella By Starlight by Sharon M. Draper

Countdown by Deborah Wiles

One Crazy Summer by Rita Williams Garcia

Serafina's Promise by Ann E. Burg

Realistic Fiction

Mockingbird by Kathryn Erskine 

I am Malala by Malala Yousafzai  

A Mango Shaped Space by Wendy Mass 

The Red Pencil by Andrea Davis Pinkney

Counting By 7s by Holly Goldberg Sloan

Three Times Lucky by Shelia Turnage

Almost Home by Joan Bauer

I, Emma Freke by Elizabeth Atkinson

Esperanza Rising by Pam Munoz Ryan 

Out Of My Mind by Sharon Draper 

Faith, Hope, and Ivy June by Phyllis Naylor Reynolds 

Love, Aubrey by Suzzanne LaFleur

Cornelia and the Audacious Escapades of the Somerset Sisters 

Sorry, I just want to point out something realy quick: I am Malala is an autobiography written by Malala Yousafzai, and her experiences in the book, getting shot, her recovery, actually happened. I really don't think that it classifies it as Realistic Fiction.......

Wow! This list already has so many of my faves! I compiled a lengthy list of some of my favorite classics (not including Jane Austen books, becasue I'm pretty sure everyone knows about them). http://www.cricketmagkids.com/chatterbox/blababoutbooks/node/238908 if you can skip through the whole long list, there are some great books there! Except for the ones that I marked "it's boring, don't read it." I'm not sure what I thought was the point of that :P 

As for some more reccomendations:

~The Princess Bride* 

This is a wonderful and really fun novel! I totally reccomend it! Especially if you''ve seen the movie. Buttercup is a wonderful female character, but don't read it if you don't like a lot of romance. 

~The Secret Life of Bees* 

This is a super book that takes place right around where I live, actually. It's about a girl trying to find out more about her mother, and she ends up at a place where her mother had stayed as a girl, and meets three quirky bee-keeping sisters. I love this book soooo much. It's actually very special to me because

A. Although I discovered it after starting my own novel, I realized that the two share a couple similarites. Both are about girls trying to discover more about their mothers.

B. My mom read it first, with a pen in hand, and she wrote a lot of little notes here and there, and scribbled out a bunch of stuff.

Yes, there is some cursing (apparently, judging from all the scribbles), but it doesn't overshadow the story's powerful morals.

~I think someone already mentioned Listing for Lions. Read it!!! It's awesome!!

~Summer and Bird

This book is about two sisters, Summer and Bird, who discover a hole that leads into another world. It's poetic and surreal, with a lot of sybolism and complications. The best part is that there isn't a ton of violence and romance to take away from the deeper story.

~School Story

Have you ever wanted to be published? Well, this book is about every young author's dream coming true. I've read it sooooooo many times, and it inspires me every single reread.

~The Lunar Chronicles! Yayyy! I think someone already reccomended them, but they are really, really cool.

~Howl's Moving Castle*

This is one of the funniest fantasy novels ever! It's about a girl named Sophie who doesn't think she is anything special, and knows that she will never find adventure, because she is the eldest of three sisters. But when she is cursed by a witch, she is forced to flee, and stumbles upon an enchanted castle owned by the arrogant Wizard Howl, and run by the fiesty fire demon, Calcifer. I actually have a Howl's Moving Castle shirt that says, "May All Your Bacon Burn!" 

~The Goose Girl

Have you ever heard the story of the princess who was forced to become a goose girl because of her evil maid? This is a retelling of that story with memorable characters, wonderful worldbuilding, and beautiful writing.

~Anything by Jane Austen*

Because she's awesome. If you're looking for a super strong, super fun girl lead, all her. books are great, but Emma is probably the wittiest and most charming.

Books with *'s have EPIC movies!!!  

The Golden Compass! The main character in the first book is a girl named Lyra, and it's one of my favourite series of all time. She is joined by a male protaginist in the second and third books, but she still remains equally important. It's by Phillip Pullman

The Shadowhunters and Infernal Devices series by Cassandra Clare both have females as the mc's, though I wouldn't read them unless I were at least 13 or 14

Wildwood, by Collin Meloy

My Sister's Keeper, by Jodi Picoult, though again only if you are at least 13.

A Wrinkle in Time, and all the books that follow, by Madeline L'Engle (there's a movie coming out!)

Whoever said To Kill a Mockingbird (by Harper Lee) I 100% agree with. It's an amazing book.

The Hate U Give (Angie Thomas) I only just started it but there's a strong female protagonist, only read it if you're at least 13 or 14.

Egg and Spoon, by Gregory Maguire 

The Two Princesses of Bammare by Gail Carson Levine and The Girl Who Could Fly by Victoria Forester. They are probably, if I was forced to choose, my all-time favorite books. The first one sounds bad and fluffy and predictable, but it's really good. Happy reading!