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.

Why were women important in Shakespeare's plays?

If plays are a reflection of life and the people who live life, then women are essential.  Shakespeare was a great observer of the human condition.  Women are a part of that.

In his comedies, the women are important because he is able to show us strong, intelligent, and independent women.  Most of the male characters don't truly understand what love is until they meet one of these women (often disguised as males).

Many of Shakespeare's plays deal with love and how can you have a Romeo without a Juliet?  Where would the great love of Antony be without Cleopatra?

Where would the play King Lear be without his daughters.  Father and son relationships are quite different from father daughter relationships.  Shakespeare had two daughters.

I could go on but the answer should be obvious.  Women make up more than half of the population.  They are lovers, wives, mothers, daughters, sisters, etc.  Shakespeare gave us all of these.