It's difficult to give a definitive answer to this question, because the circumstances surrounding their deaths are the result of misunderstanding, impatience and fear, as well as timing and circumstance. One could say Romeo and Juliet themselves are responsible for their own deaths, since both of them commit suicide. But the hateful feud that divides their families and compels their parents to forbid them to see each other is also a factor. Tybalt, Juliet's cousin, kills Mercutio, Romeo's best friend, and Romeo kills Tybalt in a fit of rage, and is banished. So on some level Romeo's behavior sets in motion the events that lead to their deaths: their plot to run away, Juliet's staged death helped by the Friar, missed communication keeping Juliet's plan secret, and Romeo's misunderstanding of it that prompts him to kill himself. Since Romeo is characterized as fickle and impulsive, he could be said to be slightly more to blame. But the final lesson of the play is that the hatred of the families for one another is ultimately the cause of their deaths.