How are Shakespeare's plays categorized?

In general, Shakespeare's plays fall into four categories.  These categories can vary, and the plays within them can vary, but for the most part these are the subcategories of his Renaissance plays:

1.  Tragedies: These plays, of course, represent the downfall of a tragic hero with all the common elements of a tragedy.  Examples include Romeo and Juliet, Othello, and Macbeth.

2. Comedies: Unlike the tragedies, Shakespeare's comedies end happily, almost always with a marriage. Examples include The Taming of the Shrew, Much Ado about Nothing, and Two Gentlemen of Verona.

3. Histories: While these plays normally fall within the bounds of a tragedy because of the hero's tragic downfall, flaw, and realization, they also focus on real-life figures, such as Shakespeare's Henry V, Richard III, etc.

4. Romances: The rarest of Shakespeare's plays, the romance blends tragic elements with a happier ending.  A Winter's Tale is the best example of this, and some literary critics would place The Merchant of Venice in this category because while it ends happily for the couples; it is tragic for Shylock, and Antonio--another main character--retains his melancholy outlook at the play's conclusion.