Did anyone mention Oerba Yun Fang from Final Fantasy XIII? At first, I didn't like her but I didn't dislike her, similarly this is how I felt towards Oerba Dia Vanille . . . Anyway, she grew on me and Fang is really independent. She does not care about what others thinks except if it's in good intentions like happiness, saving the world, etc. By nature, Fang is just strong, physically and mentally. There's no tragic events that cause her to become who she is. There's not many scenes that use her weaknesses to build her strengths. She's just Fang.
Monica Raybrandt from Dark Cloud 2. I don't know, but she was likable from the beginning. And her voice actress, Anndi McAfee did an amazing job. There's this sort of understanding and unrelenting force behind her. She's stubborn at times but she's also reasonable with many things. And considering the whole "I'm from the future in ruins" thing, Monica is wise beyond her years.
Ashelia "Ashe" B'nargin Dalmasca and Fran from Final Fantasy XII. Simply put, these two were of prestigious birth; Ashe was a noble and Fran was from the Wood. They abandoned that identity for the better good. Fran was usually calm about everything. Anything she did was smooth. Ashe as far as I remember was really dynamic. She let's her heart be heard.
Lyndis from Fire Emblem. As far as I am in Fire Emblem, Lyn just does what she wants, usually. She has dignity and integrity while not coming off as arrogant, proud, or snobbish.
Carmelita Montoya Fox from the Sly Cooper series. Despite having inconsistent voice actresses, Carmelita's relationship with Sly is funny. She commands basically everyone. At one point in Thieves in Time, Carmelita seems to be the one wearing the pants in the relationship; ironic since Sly looks like he's not wearing pants and Carmelita in Thieves in Times wears a skirt. But, Carmelita isn't as cold as everyone thinks. She's a good cop who knowing her criminals treats them humanely if they deserve it. Like Clockwerk would not get that treatment, but Bentley and Murray would. Sly's an exception since he's almost like a pest to her.
Maya, Lilith, Tiny Tina, Mad Moxxi, and I guess Ellie and Patricia Tannis from Borderlands series. Everyone in this series is crazy. Crazy good, crazy bad, or just plain crazy. And that's what makes them so interesting.
Chloe Frazer from the Uncharted series. Eh, she's like Fang I guess and I'm not saying that because they both have Australian voice actresses.
Olga Gurlukovich from the Metal Gear franchise, specifically Solid 2: Sons of Liberty. Olga is the perfect example of a loving mother. She'll do whatever to protect her child, Sunny. And sadly and cruelly, she never even got to meet Sunny. Talk about evil unto a mother.
Momohime from Muramasa: The Demon Blade. Okay, so you don't play as her much; you play as Jinkuro Izuna who possesses her body. Momohime, not Jinkuro-Momohime, is the sort of person who can forgive despite however grave something is. She forgave basically everyone and reasoned their actions. Because of this, some people slowly changed their ways by her example. Revenge is easy, forgiveness isn't.
Aqua from the Kingdom Hearts series, specifically Birth By Sleep. Typical wise, rational, and powerful person. She sacrifices many things to save her friends. At the same time, she's one of the most powerful magic users in the series. Aqua's no pushover when it comes to fighting.
Eirika from Fire Emblem: Sacred Stones and almost every female character in the Fire Emblem series. Fire Emblem, I think is one of the few series out there that have more than a handful of female main characters in each game or the series as a whole. I don't know much about Eirika though, but I know that her brother, Ephraim was said to have the potential to be the most powerful Lord in the series. But I might have heard wrong.
Female (and male) Shepard from Mass Effect. You define her/his character. Of course she/he is epic. Unless you intentionally make a crappy Shepard. Then that doesn't apply.
Rosalina from Super Mario Galaxy 1. I don't know. I just like her. Mother of all Lumas, well, surrogate mother.
King from the King of Fighters franchise. Let's see, she's French and fights with a Muay Thai, kick-boxing, and potentially Savate fighting style. The only thing is that she tries to hide her gender for some reason that escapes me. Otherwise, she kicks ass.
Leanne from Resonance of Fate. She's funny with a twisted past. I'm running out of things to say as this drags on, sorry.
Seth Balmore from Lost Odyssey. An immortal warrior who also happens to be the mother of a man twice her physical age - she's immortal and her son "being" older not being obvious enough . . . I don't know what to say. The game talks about the price of immortality and her story revolves around that too. Shame that Lost Odyssey was only for the Xbox 360 and a PC port never made it into existence.
Katherine "Kate" Marlowe from Uncharted 3: Drake's Deception. She apparently is a devious villain compared to other villains from past games. Marlowe knows and has everything to break you and make you do anything for her.
There's obviously more, but I've run out of what to say. Tales series, Persona franchise, Catherine, inFamous, Ratchet & Clank, Jak & Daxter, other Final Fantasies, etc.