In Shakespeare's Romeo and Juliet, it is important to uncover the several ways in which this tragedy comes about.
In the Prologue we are informed that Romeo and Juliet are star-crossed lovers. Fate is against them, and they are destined to die. With this in mind, other characters may be used to drive the plot or lead characters to certain actions, as was Shakespeare's wish. He tells us the ending—and that Romeo and Juliet are not to blame.
Many look to put the responsibility for the tragedy on Friar Lawrence. However, in some ways, this is like suing the Good Samaritan. Romeo is ready to kill himself, Juliet is ready to kill herself rather than marry Paris, and the Friar wants to help these two, hoping that the feuding parents might change through their children's love. Ironically, he is not that far off the mark: Romeo and Juliet's relationship does change things between the Montagues and Capulets; unfortunately, it is their death that makes the difference. It's important to remember that these young people make up their minds to live together or not at all. Though young, they go to the Friar, each one, with eyes open.
Difficulty does arise with the Friar, first with the secret marriage. Next is the arrangement he makes with Juliet to bring on a death-like appearance. In Act Four, scene one, Juliet visits the Friar. Juliet makes it clear that she is willing to stab herself right there to avoid marrying Paris. The Friar observes that if she is willing to kill herself, she should also have the strength and willingness to take a potion to make her look dead, and wait to be "rescued" by Romeo.
…If, rather than to marry County Paris,
Thou hast the strength of will to slay thyself,
Then is it likely thou wilt undertake
A thing like death to chide away this shame,
That cop’st with death himself to scape from it;
And, if thou dar'st, I'll give thee remedy (IV.i.72-77)
Sources lay some blame at Prince Escalus' door. For all the time there has been a feud going on, Escalus has acted like the threatening parent that says, "If you don't stop it, I'm going to…." over and over. After a while, no one listens; but in Act One, he threatens the families with death.
If ever you disturb our streets again,
Your lives shall pay the forfeit of the peace. (I.i.92-93)
When Escalus finally takes a stand, he ends up banishing Romeo because he had killed Tybalt, who had killed the Prince's cousin, Mercutio. However, in banishment, Romeo and Juliet are separated, and a breakdown in communication between Friar Lawrence and Romeo causes the newlyweds to take their lives.
Personally, I blame Capulet as well. At the beginning, he tells Paris to wait two years to court Juliet. Even then, he says that Juliet will have the last word in whether there will be a marriage.
But woo her, gentle Paris, get her heart;
My will to her consent is but a part.
An she agree, within her scope of choice
Lies my consent and fair according voice. (I.ii.16-19)
By the end of Act Three, Capulet had completely changed his mind and promised Juliet's hand to Paris.
Thursday let it be— a Thursday, tell her
She shall be married to this noble earl. (III.iv.21-22)
When Juliet refuses, Capulet's rage descends on his daughter and he threatens first to drag her to the church; next he threatens to throw her out into the streets. In light of this, Juliet turns to Friar Lawrence for help. (Remember, too, she is already married, and cannot marry Paris also.)
Perhaps the character with the greatest blame is Friar Lawrence: whilst his intentions are good (if you ignore the fact he is going against the wishes of the family), his plan is misguided and liable to fail. He warns Romeo "they stumble that run fast" and yet encourages them in their hasty marriage (although the pressure is put on them by the impending marriage to Paris).
This leads on to the next two characters - Montagu and Capulet, and all their ancestors who have contributed to this "ancient grudge".
Ultimately, my own view is that 'no-one is to blame, and everyone is to blame.' That is why Shakespeare continues to engage us, because we are intrigued by the ambiguity.