William Shakespeare's plays can be categorized into the comedies, tragedies, and histories.
Romeo and Juliet is considered a tragedy because our heroes suffer a terrible downfall and sorrowful end. Romeo and Juliet both commit suicide, Mercutio, Tybalt, and Paris are all murdered, and the Capulets and Montagues are left to mourn the loss of their dear family members.
After Romeo is told that Juliet is dead, he proclaims, "I defy you, stars!" which gets to the heart of the tragedy of Romeo and Juliet. Romeo doesn't blame circumstance or bad luck for his true love's tragic end, but he blames the stars because he believes that everything is destiny and pre-determined. Romeo is frustrated because the heavens took Juliet from him just as quickly as they brought her into his life, and he has now his true love. This is a major theme in the play and only heightens the tragic drama of the lovers' deaths.
Though Shakespeare himself wouldn't have understood this play as a "Romance," our modern terminology and understanding of genres could easily classify this play as a "Romance." Modern romance stories focus on the development of a relationship that does not always end well. For example, Baz Luhrmann's film adaptation of Romeo and Juliet appeals to our modern sensibilities of romantic relationships by setting the play in a modern context. More than anything else, this modern adaptation focuses entirely on Romeo and Juliet's passion and devotion to one another more than any other relationship in the play.