Did William Shakespeare have a favorite personal play?

This is an interesting question, but a difficult one to answer. William Shakespeare left very little personal information behind, and much of what is known about him is inferred through secondary historical resources.
In fact, we do not even know of all of Shakespeare's works. Many were lost in the fire that burned down the Globe Theatre in 1613. Others are likely unattributed to him since it was not a common practice at the time for playwrights to sign their works. He also frequently collaborated with other playwrights, and these contributions are even less well-documented than his 37 known plays. Without a full catalog of Shakespeare's works, it is difficult to even speculate on which work might have been his favorite.
This is made even more difficult by the lack of personal information about William Shakespeare. He did not leave a journal that we know about. Almost no personal correspondence to or from him survives, and what does refers to mundane or business related matters. In short, there is no known instance of him declaring which play of his was his favorite or even any solid hinting. Therefore, barring the discovery of a new primary source, we will never know which play of Shakespeare's was his favorite.