Who or what caused the death of Romeo and Juliet? What are three quotes that prove this?

Literally, they killed themselves. Romeo by drinking poison and Juliet by stabbing herself. Thinking that Juliet is dead, Romeo decides that it is better to join his love in death than to live without her. He illegally purchases poison from an apothecary and drinks it over her as she lays in her tomb. After he drinks the poison he says,

O true apothecary!Thy drugs are quick. Thus with a kiss I die. (act 5, scene 3)

When Juliet awakes from her potion- induced false death she finds Romeo dead in her tomb. She scolds him for not leaving enough poison for her. Instead, she takes his knife and plunges it into herself.

O happy dagger!
This is thy sheath;
there rust, and let me die. (act 5, scene 3)

Less directly, the feud between the Capulets and the Montagues causes the death of Romeo and Juliet. The inability of the two families to put aside their differences means that there can be no hope for their children's love. In this sense, the parents of the two lovers are to blame. After they first met at the Capulet party, Juliet says that if only Romeo were not part of her enemy's family there would be no impediment to their love. She remarks that if their names were different, then they would be alright.

O Romeo, Romeo! wherefore art thou Romeo?Deny thy father and refuse thy name;Or, if thou wilt not, be but sworn my love,And I'll no longer be a Capulet. (act 4, scene 2)

Even the Prince sees himself as responsible for their death. In a very indirect way, he is. He feels that he could have ordered the Capulets and the Montagues to end their feud. He says,

See, what a scourge is laid upon your hate,That heaven finds means to kill your joys with love.And I for winking at your discords tooHave lost a brace of kinsmen: all are punish'd. (act 5, scene 3)