Who was to blame for Romeo's and Juliet's deaths?

I would argue that their deaths are the fault of their parents.  After all, it is the feud between their parents that initially makes Romeo and Juliet off limits to one another.  If the Capulets and Montagues weren't fighting, their children would likely have been able to be honest about their mutual love.  However, that is not possible because, as they are aware, their families would never accept the relationship. 

Further, Juliet is driven to desperate means due to her parents' threats and demands.  If they were not attempting to force her to marry the County Paris against her will, she would not go to Friar Lawrence's cell begging for his assistance, he would never concoct his plan, and she would never fake her own death, an action that leads to a miscommunication of epic proportion that results in Romeo's suicide by poison, an event that leads to Juliet's suicide by dagger.  Lord Capulet is brutal to his daughter, insisting that he would let her die in the streets before he would ever help her again if she disobeys him.  If he and his wife didn't push Juliet, she would not have taken the drastic measures that resulted in her own and her husband's deaths.