I'm sure this topic has been done here before, but probably not for a while...I searched the first few pages here and didn't find one. (Maybe I should've used the search function, but whatever, stfu)
Anyways, I got the idea from the "favorite female fronted band" topic in the music forum.
My favorite female character would have to be "The Boss" from MGS3. She's such a strong character that sticks to her convictions no matter what. She's both a hardened soldier that you feel respect for (I mean, shit, she's considered the GREATEST SOLDIER IN THE WORLD), yet at the same time is one of the most sympathetic characters I've ever seen in a videogame. Maybe more of her background with Snake could have been fleshed out in MGS3 but ultimately you understand her significance in the whole picture of the MGS universe. What I like about her too is that she's not the typical stupid bimbo girl, or the "tee hee hee I'm cute and japanese and all the little boys have fantasies about me and my eyes look like this ^_^ LOL". I'll mention more specific details as spoilers, though I'm sure if you're an MGS fan you've played MGS3 by now:
(mgs 3 spoilers below)
[spoiler]The Boss had to cope with the loss of her son (Well, we all know who this is now...Ocelot OMG) who was taken away by the patriots/philosphers. After going undercover, Volgin completely fucked up her mission by firing the Davey Crocket...which then changed her mission from stealing the philosophers legacy, to die by the hands of Snake to avoid a nuclear conflict with the Soviet Union. She accepts this mission, as she embodies the "ultimate soldier" mythos in the truest form created by the MGS universe. Her mission is to be killed by the hands of her greatest disciple (there's another word I'm thinking instead of "disciple" but it's 3:30 and I can't think straight haha...maybe it IS the right word I'm thinking of), as well as be blamed for the nuclear explosion and be remembered as a traitor to America after her death, even though the truth is that she was a true patriot.
It was amazing hearing The Boss completely open up to Snake during their final battle, because she always came across as strong willed, and masterful at handling her emotions. Telling Snake the emotional pain she went through and seeing a tear run down her face, all due to her duty as a soldier, was just incredible. Then the later revelation about the true nature of her mission was just icing on the cake. I couldn't believe how deep this character went...not only is she one of my favorite female characters, but one of my favorite characters in general.
Not just the character, but the placement in the MGS story is incredible too. Basically, the final battle between Snake and The Boss, Eva's confession to Snake, and Snake being awarded the "Big Boss" title all led to the time where Big Boss turned against America, and turned against fighting for someone else's agenda. It was mostly the fact that America easily disposed of one of their most important and beloved soldiers in their history, and also reviled her name after her death. Even though she saved America, she would always be remembered as a traitor and a terrorist, and those events would ultimately lead Big Boss to create Outer Heaven.[/spoiler]
My other favorite female character is probably gonna be mentioned by everyone, which is Xiuying from Shenmue II. I'll keep this brief because I'm sure everyone knows all the background, but I like her for the main reason's I like The Boss. Strong willed, a strong fighter, not a stereotypical bimbo type character....also a leader, a teacher, and a voice of reason. She also comes across as a sympathetic character because of Ziming, and being exposed to a moment of emotional vulnerability makes you connect with the character so much more.
Honorable mentions: Shenhua (It's tough because there really hasn't been alot of time she was in the series...this is why we need Shenmue III dammit!!!).
Millenia - Grandia II (Ok, she does kind of play into more of the bimbo-ish thing I was talking about, but she provides alot of comic relief and also doesn't fuck around.)
Bastila - KOTOR (I dunno, just an awesome character + hot british accent)