There are many characters in the media, both male and female. While some adhere t the stereotypes placed upon their gender, some go directly against them. Here are some examples of some men and women who both challenge and adhere to their gender's stereotypes.
Male and female characters adhering to their gender's stereotypes:
Male
Jack Shepard (from TV's LOST) fits the male stereotypes. He is a strong character who leads the group.
Female
Shirley Bennett (from TV's Community) perfectly fits the stereotypes placed upon her gender. Shirley lives to serve her family and is deeply religious. She is also obsessed with cooking and baking. Shirley is the perfect stereotypical housewife.
Male and female characters challenging their gender's stereotypes:
Male
Morgan Grimes (from TV's Chuck) challenges several stereotypes placed upon the male gender. Generally, males are seen as the stronger gender. Morgan counters this stereotype as he is incredibly week and not brave (he squeals regularly). males in the media also, usually, control situations. Morgan counters this as he is never in control.
Female
Sarah Walker (from TV's Chuck), while remaining a sexual object for the male gaze, does challenge several gender specific stereotypes. For example, Sarah's primary role within the show is as a spy. This results in a lot of fighting. She fights the same way as the men in the show, removing the stereotype hat women are weaker than men. In addition there are several scenes in the show, such as clips of her cooking, that challenge the stereotype that all women occupy the position of housewives and are skilled at remedial tasks like cooking and cleaning.