First, the title of play would make no sense whatsoever, if zero characters were named Juliet.
Second, if Juliet were not in the play, then Romeo would not have met her at the Capulet party. That would be terrible, because then the audience would be forced to listen to Romeo whine about Rosaline for who knows how many scenes. In fact, the play would likely be called "Romeo and Rosaline." The plot would be entirely different, because Romeo would spend all of his time trying to convince Rosaline to not be a nun.
Of course Romeo might be alive at the end of the play too, since he wouldn't have a reason to kill himself.
If Juliet were not in the play, then Capulet wouldn't have to hastily arrange a marriage to Paris. Paris wouldn't need to go to the tomb; therefore, Paris wouldn't die.
If Juliet were not in the play, then Romeo wouldn't have secretly married anybody. No secret marriage. No relationship with Juliet. Nothing. That would possibly cause Romeo to fight Tybalt right away. Tybalt still dies though, but Mercutio would be alive. Or perhaps that entire exchange doesn't happen. Tybalt lives. Mercutio lives. Romeo lives.
If Juliet were not in the play, then the Capulets and Montagues would still be fighting. Romeo and Juliet's death causes the two families to call a truce. No Juliet = no death of Romeo and Juliet = no truce.