Kahlan Amnell (Sword of Truth books by Terry Goodkind)
Eve Dallas (In Death series by Nora Roberts)
Susan Ivanova (Babylon 5)
Lyta Alexander (Babylon 5)
Lagertha (Vikings television series)
Dagny Taggart (Atlas Shrugged)
Criticisms
A common criticism is that (some) strong female characters are one-dimensional.
Oft-cited problems with individual strong female characters include:
her strength is in martial arts, but she has no strength of character
she still has to conform to gender-normative standards of attractiveness
she will wear skimpy or fetishistic gear to fight in, and her battles and acts of heroism will be presented to the audience as erotic spectacles.
she will be strong right up until she can't deal with something and has to be saved by a man
her strength is diminished when she gets interested in a member of the opposite sex
her strength is primarily a narrative tool to measure a male protagonists' progress in his emotional maturity plot arc, in which his full maturation is signaled by getting the girl, and her interior life or own motivations are not portrayed (such female characters often feature in works that fail the Bechdel test)
she objectively has the power and skill needed to solve the work's central problem herself, but she is instead required to act as mentor, sidekick, or love interest to an initially less-effective male Chosen One (often referred to as "Trinity Syndrome" after the character from The Matrix).
she has no close female friends or female allies, and disdains "weaker" or more conventionally feminine women for not being "badass" (this is often a problem in works by less thoughtful male writers trying to create a "women can fight too!" character, whether motivated by sincere egalitarianism or a desire to titillate).
A more general problem with the concept is that, especially in geek media, "strong female characters" are often defined as "strong" purely in terms of having outstanding physical strength and combat ability. This arguably devalues other forms of "strength". It also validates violence as a means of resolving conflict, which is rejected by many strains of feminism.
"You know what's a problem? Strong female characters. First of all, why do we have to specify "strong" when referring to "female characters?" Why is this not a given? The default for male is not "strong" or "wusstastic," so why do we have to be so specific about the chicks?"
Hark a Vagrant comic - Strong Female Characters by Kate Beaton. Created together with Carly Monardo, Meredith Gran - The comic parodies the popular treatment of female characters in American comics. Beaton highlights the practice of giving characters a veneer of physical strength or skill, which is seen to somehow mitigate otherwise highly sexualized and stereotypical traits.
Hopeful Upcoming Characters
These characters have yet to make an actual debut but so far seem that they may have interesting, good, or unique characteristics to add to the female character grouping. - To be looked at later