What is the moral behind the story in Romeo and Juliet?

The moral of Romeo and Juliet is one of letting old family wounds go, and not letting your emotions rule your life. The Montague and the Capulets have let an old family rivalry take over their lives. They refuse to have anything to with each other. They are both a very powerful and influential, but they have such hatred for the other. 

If the two families had let the rift between them go, then they may have been able to save the lives of their two children. If they had allowed Romeo and Juliet to be able to have an open relationship and not make them feel like they have to hide their relationship, then the two families could have come together and had a great life together. If Romeo and Juliet had been a little more patient with their relationship, and given their parents time to maybe come to an understanding, then they wouldn't have lost their lives. The whole moral is to let go of the things in the past, and to keep control over your emotions. The opening lines of the play tells how the hatred between the two families led to the death of their beloved children.

"Two households, both alike in dignity, in fair Verona, where we lay our scene. From ancient grudge break to new mutiny, where civil blood marks civil hands unclean. From forth the fatal loins of these two foes, a pair of star-crossed lovers take their life. Whose misadventures piteous overthrows. Do with their deaths bury their parent's strife. The fearful of their death-marked love. And the continuance of their parent's rage, which, but their children end, nought could remove, is now the two hours traffic of our story. The which if you with patient ears attend, what here shall miss, our toil shall strive to mend."

If the parents had put aside their hatred and let Romeo and Juliet be together, then the whole family could have come together and shown the world how strong family could be.