Oh, boy... err... "girl". So many choices, aren't there?
Kazooie (Banjo-Kazooie)
http://images.wikia.com/banjokazooie/images/4/48/KazooieTooie1.png
Kazooie is capable of working as a team or literally "flying solo". She can manipulate the strangest objects into tools for her own use, or even strangely become various types of tools for Banjo's use. She tells it like it is, be in positive or negative (though, she would prefer that it be negative).
GLaDOS (Portal)
http://upload.wikimedia.org/wikipedia/en/b/bf/Glados.png
I think she counts. Robots count, right? Frankly, I could totally see her getting along well with Kazooie. She's also very manipulative, yet wants to give you exactly what you want, while it's something you don't want, somehow. I dunno. She might plant the desire for something (notably, cake) in one's mind, and along the way, they really want and really don't want what she has to offer. She's also got multiple personalities in her subconscious, has so much fun with life, yet finds killing to be a most useful tool, she's very professional, yet unprofessional, at the same time and... Gee. GLaDOS is just a paradoxial genius, isn't she?
Talwyn Apogee (Ratchet & Clank)
http://en.ratchet-galaxy.com/images/racod/personnages/Talwyn.png
She's become very much like her father, yet isn't what you would call a "Daddy's girl". She tends to be somehow calm, yet fierce. She'll make sure everything about a situation is understood by everyone present. She also users her head in conflict, yet easily slicks right into combat. Oddly enough, for the longest time, I didn't even notice she had a tail. In fact, just typing this up and finding her picture, I happened to notice her tail has a bit of a spear shape, rather than resembling a rats' tail, like I'd previously thought. Totally weird.
Toph (Avatar: The Last Airbender)
http://fc08.deviantart.net/fs71/f/2010/319/2/2/toph_by_angel624626-d32xat3.png
She has been my favorite character in this series for quite some time. She's the smallest drill sargent I've ever seen. She tends to mess with your mind to get you to learn something important, and she she sees to it that she makes you stay "learned"! She tries to come off as simple, but when she really opens up, becomes a much deeper, more complicated person. She doesn't discriminate. She won't hate you for ethnicity, age, gender, or anything like that. If she hates you, it's because you did something stupid. Really stupid. As such, If someone does something stupid, she'll let them know it the most sudden, blunt, (and slightly violent) way possible, without warning, regardless on any such status of ethnicity, age, gender, or any of that stuff. She's totally smooth with change; constantly expanding her horizons on anything she understands. Ironically, she's blind.
Twilight Sparkle (My Little Pony: Friendship is Magic)
http://media.animevice.com/uploads/0/69/512625-void_0_.png
Now, how could I forget my most favorite female character of all? She's intelligent, modest, geeky, wise, and full of integrity. Twilight researches various topics almost constantly. She has a wide variety of friends who are little-to-nothing like her or each other. She tries to keep things positive, yet doesn't resort to fudging it up. So, in a sense, she's actually a lot like me... except for the parts about her being a quadrupedal, magical talking unicorn-pony-girl. She's gentle in most scenarios, but when serious times call for serious business, she'll jumps at the chance. She's a completionist, and keeps very organized. She makes an effort to meet deadlines, while leaving no detail undone. But she may freak out more over something being incomplete and on time than something complete and late. She strives to understand as much as she can, both terms of practical knowledge and social involvement. She thoroughly understands common sense, and would like for everything to make sense. She'd rather be in a group than to be alone, and spends her time trying to learn and understand anything and everything.
I have some honorable mentions; some of which I haven't explored all that much yet, such as Samas Aran from the Metroid series, Major Motoko from Ghost in the Shell, Alyx Vance from Half-Life 2, Laura Croft from either incarnation of Tomb Raider, and this relatively-new character out there, who is known as "Bayonetta".
Samas Aran
http://samus101.files.wordpress.com/2010/05/samus_aran_hires11.jpg
Major Motoko
http://www.ucandaire.org/imaj/mnc/kusanagi.jpg
Alyx Vance
http://borderhouseblog.com/wp-content/uploads/2010/05/alyx_vance.jpg
Laura Croft
http://www.lyricis.fr/wp-content/uploads/2011/11/Tomb-Raider-Lara-Croft.jpg
Bayonetta
http://animestuff.files.wordpress.com/2010/01/bayonetta.jpg