This, as you are probably aware, is quite a large topic, one that books, in fact, have been written about. A book I would recommend for more detailed research on this question is As She Likes It: Shakespeare's Unruly Women by Penny Gay for Routledge Press.
Here are a few general observations to get you started:
- Shakespeare worked in a theatrical world in which women did not perform onstage. The use of boys and men to play the female characters affected Shakespeare's creation of his female characters, many of which are strong and quite masculine in their natures. Shakespeare, we can assume, took inspiration from the underlying real masculinity of the actors playing these strong female characters -- characters like Lady Macbeth, Juliet, Beatrice in Much Ado, Kate in Taming of the Shrew and Cleopatra.
- There are female characters in Shakespeare's plays who are important to the story, but who do not have, relative to the male characters in the plays, a very prominent speaking part. Hero in Much Ado, Desdemona in Othello and Ophelia in Hamlet fall into this category. These characters are onstage in many scenes in which they say very little and are important to consider in that they represent, for the most part, the more traditional females from Shakespeare's society.
- The women in Shakespeare's plays have had a profound effect on characters who have come after them in literature. Also, we still, today in 2010, can see many of these characters performed and feel a strong connection to and understanding of the situations and feelings of these women. This speaks to the breathtaking universality of the women created by Shakespeare.
Please follow the links below for more discussion of and information about the importance of women in Shakespeare's plays.