All of the above. As the Prologue provides a summary of the play, it is stated that these are
1. "star-crossed lovers," - It is chance that Romeo spots Juliet and becomes infatuated with her. It is chance that Romeo comes into the street and happens upon the quarrel between Mercutio and Tybalt, thus effecting his banishment after he vengefully kills Tybalt, and it is chance that the plague falls upon Mantua and Romeo does not receive the message for him. It is even chance that the guards come and Friar Lauence runs off and is, then, not present to prevent their suicides.
2. They have "misadventured piteous overthrows." Romeo and Juliet both speak impulsive words in the orchard scene, they are quickly and secretly married, Romeo in sudden anger slays Tybalt, an act which banishes him from Verona, Juliet drinks the vial prepared by Friar Laurence, and they both commit suicide.
3. They suffer from "their parents' rage." It is the "ancient grudge" which begins the problems that Romeo and Juliet first encounter, and from then on, complications of this feud effect the major conflicts in the play.
It's definitely their own fault. They were too young and too impetuous and lacked the maturity to think through the consequences of their actions. The first post is right in that many people had a hand in creating the circumstances that led to Romeo and Juliet's deaths. However, the basic reason was that the two of them became so infatuated with one another that they never stopped to think about what they were doing. Other options were open to them, but they never looked for those options.