Matilda all the way. Reading about a smart, entirely capable young girl while I was one myself was super empowering and I still remember imagining that I could move things with my mind.
There are more recent favorite female characters of mine, but she was the first to have a memorable impact on me.
Lisbeth Salander from the Millennium Trilogy and the Woman from Sherlock Holmes! There are so many though....
Annabeth from the Percy Jackson series. She's a strong person, she's tough, and she never forgets to be awesome. :)
Pride and Prejudice: Lizzie Bennet, as imperfect as she is <3
Circle of Magic (Tamora Pierce): Tris and Sandry. Both dedicated to their friends, and taking no crap from anyone. I adore the idea of young girls reading characters like these and thinking "that girl is awesome. I want to be like her"
In Death series (J.D. Robb): Eve Dallas and Peabody. Because awesome cops who kick butt and drip with sarcasm with idealistic/ tragic pasts working the mean streets of NYC as partners hits all the right notes for me.
I am currently reading a high fantasy novel called "Mistborn: The Final Empire". The main character of the series, Vin, is a strong female character who is a quick thinker and, by using her brain and her extraordinary abilities, can get out of any situation. She kind of reminds me of Katniss a bit- they both have similar personalities.
Alaska, because I thought she was a great character, and even though she wasn't the best girl (by any stretch) she is still one of my favorite fictional characters. I like her, because I kind of like those kind of girls. Not the drinking, smoking, addicted to sex type of girl, but the sporadic type, adventurous, and making me do things that I wouldn't otherwise do type of girl.
Hmm... perhaps Dagny Taggart from Atlas Shrugged for her independence, intellect and strength. On the other hand there is Kitty from Anna Karenina who is just precious.
Isabelle Lightwood from the Mortal Instruments series, because she kicks butt :)
I've had lots but at the moment it is Celaena Sardothien from Throne of Glass for her intelligence, strength of the mind and independance.
Katniss Everdeen and Margo Roth Spiegelman
Keladry of Mindelan, Protector of the Small series, Tamora Pierce.
She's strong, determined, but still human. She isn't perfect, gets angry, reacts wrong, makes bad decisions, but always goes on. She may be like other female characters, but she is human in a way I can understand and relate to. Also, she is a character of my favorite autor. Sorry John.
i find it very hard to choose between Annabeth Chase from the Percy Jackson series and Hermione, but i'm currently giving the edge to Annabeth. Both characters were extremely important to me growing.