Alita from Battle Angel Alita (or Gally from Gunnm, if you prefer that)
Not only is Alita my favorite female protagonist, the manga is also my favorite manga ever (mind you, Last Order not so much, too much padding).
Alita is strong, heroic and kind, but can also be vulnerable, pig-headed and cruel at times. Her main goal is to become the strongest fighter so she will no longer have to fight. Apart from being an awesome fighter, she's also well-read and has artistic talent (in her case music). And while she has a few love interests (and they are actually subject to change, their no one true love for Alita), she isn't defined by her romantic relationships alone, but also the father/daughter relationship she has with Ido or with the different friends she makes during the course of her story. Sex is also pretty much a non-issue here. Sure, Alita has a clearly female body, but it's all metal with no genitalia.
Throughout the story manages to gain the respect and adoration of many people, allies and enemies alike, through sheer will-power and awesome-ness.
All the days are here:
