Why was the Romeo + Juliet (1996) movie set in modern times?
It helps bring home to a modern audience what is happening in the play. Some people find that the abstraction of setting the play in an unfamiliar time and place interferes with their understanding of the themes.
By setting it in a modern day setting which is far easier to relate to it allows people to enjoy the play more easily and appreciate how timeless the themes actually are.
It helps prove the case that Shakespeare's themes and stories have a timeless quality -- especially as this version does very little to update the language. One could take the underlying story in the play and update it (a la West Side Story) but the play would not really be "Shakespeare." Only an adaptation. That a play can be set in a different time or place and still retain the beauty of the language and present a comprehensible story is a testament to the playwright and the director.