Romeo and Juliet are known as star-crossed lovers. This use of "star-crossed" refers to the tragic end that Fate has dictated for them.
First of all, it is quite by accident that Romeo even goes to the party where he meets Juliet. It is not in his plan. He finds out about the party from a Capulet servant who stops to ask for help, no knowing Romeo's identity. Romeo and his friends decide to crash the Capulet's party, and can do so because they wear masks.
Capulet, Juliet's father, does not take steps to chastise or throw Romeo out, even after Tybalt draws the older man's attention to Romeo's presence. Had he done so, perhaps the two would never have made a serious connection. It is odd, too, because we find out later in the play that Capulet is not such an easy-going kind of person after all.
The two fall quickly in love and secretly marry. When Tybalt confronts Romeo's friends, Romeo tries to stop the fight. He has no reason to fight Tybalt as they are now related. Romeo cannot tell this to Tybalt, obviously, but he does try to dissuade the Capulet from attacking. Fate steps in: Romeo refuses to engage in battle, no matter what Tybalt says; however, Mercutio has no such compunction. As he and Tybalt go at it, Romeo tries to intercede, and Tybalt takes a cheap shot, stabbing Mercutio beneath Romeo's arm, where Mercutio has no way to defend himself.
If that weren't bad enough, Romeo snaps, and in a rage, wreaks revenge against Tybalt (a Capulet, related to his wife) for his dear friend's death. In this situation, Romeo tried to do all he could to avoid bloodshed, but Fate had other plans he could not avoid.
After Romeo is banished from Verona, poor luck traps Friar John in the city so that he cannot take Friar Lawrence's note about Juliet's "faked death" to Romeo. Since the entire affair is a secret, it is also bad luck that Romeo's servant DOES arrive in Mantua to tell Romeo that Juliet is dead (when she really is not).
Romeo travels back to Verona (with poison in hand), not knowing of the plan to join him with Juliet. He believes she is dead, Friar Lawrence is late in arriving to stop it, and so Romeo kills himself. When Juliet awakes, Friar Lawrence begs her to leave with him as the watch has been raised. She refuses, and in the end she takes her own life.
All of these circumstances are the result of bad luck and poor timing, each which an Elizabethan audience would chalk up to Fate's interference with the two lovers and those around them. With Fate's hand involved, Romeo and Juliet never had a chance.