How did William Shakespeare depict women in his plays?

The way Shakespeare represents women in his plays varies wildly from play to play. This is a facet of his work that is both lauded and disliked by critics. Some believe Shakespeare has presented a diverse range of dimensional female characters, and others see his women and their fates as products of the misogyny of the time period. 

I would personally argue that the vast majority of Shakespeare's female characters possess positive, multi-faced characteristics that make them incredibly relatable even to modern readers. Women in his plays are generally presented as intelligent, strong, intuitive, independent, and defiant. They often exercise their free will to single-mindedly pursue their desires or to assert themselves and their voices. We see this in Romeo and Juliet when Juliet defies her parents and the age-old grudge match they have with the Montagues by secretly marrying Romeo instead of giving in to an arranged marriage with Paris; in Othello, Desdemona makes a similar gesture of defiance toward her father by marrying Othello; furthermore, in The Merchant of Venice, Jessica disobeys her father Shylock by running off with a Christian. 

Women often are willing to do whatever it takes to make their way through the world in Shakespeare's plays. This sometimes may involve extreme wit, guile, clever disguises, and extremely creative problem solving. In Twelfth Night, Viola assumes the disguise of a man, Cesario, in order to safely move throughout the world after surviving a terrible shipwreck. In The Merchant of Venice, Portia disguises herself as a male lawyer and literally goes to court to save the man she loves from legal trouble after a deal goes wrong with Shylock. Cleopatra makes wily romantic and political decisions to advance her own agenda and to maintain her sense of personal power in Antony and Cleopatra. 

Even the sweetness and vulnerability that can be found in Shakespeare's tragic heroines is a demonstration of the complexity of the female mind and the playwright's understanding of it. While Desdemona may gently give herself over to her husband, meekly suffocating while begging for his forgiveness, we are able to understand that this comes from a place of excruciating love and foolishness. In much the same way, Juliet's suicide over Romeo's freshly dead body is a startling reminder of the real troubles, grief, and sorrow that women experience in love. By bearing witness to women's weaker moments, Shakespeare pays tribute to their strength and provides a dimensional look at what happens when that resilience collapses. This is not misogyny, in my opinion, but rather authenticity. 

Overall, the women within Shakespeare's works are unconventional, fascinating amalgams of all that is good and bad about human nature. They possess attractive qualities and unattractive ones; they thrive and they fail; they live and die; they rule and crumble; they resist and concede; and, most importantly, they spring from the page.