The deaths of their two children, Romeo and Juliet, are the primary cause of the reconciliation in Act 5 of the play.  The two families have feuded for so long that no one can even remember why they are feuding in the first place. As the families see the final devastation of the the feud in their dead children, they realize the foolishness that caused this outcome.  The families have already seen Tybalt and Mercutio die due to the feud, but those deaths seems to be a natural consequence of the longstanding animosity and don't touch them as closely.  The deaths of the children by their own hands hits much harder.  That the children saw no other way to live and preferred death to life without the other is such a sad realization for both sets of parents.  The regrets on the Capulet side are probably even more profound in the fact that Paris is also found dead in the crypt.  If they hadn't pushed Juliet to marry someone whom she expressly stated she didn't want, then the urgency of Romeo and Juliet's actions would haven't have driven them to such extreme measures.  The ending the play provides what is traditionally considered a catharsis for the audience.  We are unhappy with the deaths, but relieved with the idea that the tragedy brings about an improvement in the overall situation.