Other than Romeo and Juliet themselves, what three characters have contributed to their deaths in Romeo and Juliet?

Three characters who contribute to the deaths of Romeo and Juliet are Friar Lawrence, Tybalt, and Lord Capulet.

• Friar Lawrence

Initially, Friar Lawrence warns Romeo against impetuous behavior, but he himself acts impulsively as he abruptly decides to perform the marriage ceremony for Juliet and Romeo in the belief that their union will be a catalyst for the ending of the feud.

For this alliance may so happy prove,
To turn your households' rancour to pure love. (2.1.91-92)

However, his plan is flawed because he performs the marriage in secret and he does not consider the fact that the resurgence of the animosity may easily prevent the two families from considering any reconciliation at this time. Instead, he should perhaps have urged Romeo to wait so that he could, perhaps, meet with the parents and ameliorate their relationship.

Friar Lawrence has contributed further to the tragedy of Romeo's and Juliet's deaths with his surreptitious plan of faking Juliet's death. His deceptions have effected the tragedy of Romeo's suicide. In addition, even though Friar Lawrence is aware of Romeo's dead body in the tomb, he abandons Juliet because he fears arrest by the guards. Perhaps he should have waited for her.

The fiery and impulsive Tybalt is indirectly responsible for the death of Romeo. At the Capulet masque, he has ignored his uncle's words to "endure" Romeo's presence, harboring his hatred until he vents it in a public place in Act III where he slays Mercutio. This act enrages Romeo so much that he, in turn, kills Tybalt, a deed that leads to his banishment and all the other tragic consequences.

• Lord Capulet

Lord Capulet is also indirectly responsible for the deaths of Juliet and Romeo because his demand of Juliet that she marry Paris has led her to taking the desperate action of drinking the potion of Friar Lawrence. This action, in turn, has placed her in the Capulet tomb where Romeo has found her and, thinking she is dead, he has killed himself. 

Certainly, Prince Escalus, along with himself, lays blame upon the Capulets and the Montagues for the tragic deaths of Romeo and Juliet:

Where be these enemies? Capulet, Montage,
See what a scourge is laid upon your hate,
That heaven finds means to kill your joys with love!
And I, for winking at you, discords too,
Have lost a brace of kinsmen. All are punish'd. (5.3.301-305)