The protagonist of a literary work is the character that the story revolves around. It is the character that the author focuses on the most. The play Romeo and Juliet seems to focus on both Romeo and Juliet equally because they are a couple; however, I would actually argue that the play focuses more on Romeo and that he is the protagonist. We can argue that the play focuses more on Romeo because he is the first character of the couple that we meet. We meet Romeo in the second half of the very first scene whereas we do not meet Juliet until the third scene. Also, in the final scene, Romeo is given far more lines before his death than Juliet. Hence, we can say that the play focuses more on Romeo than Juliet and that he is the protagonist.
The antagonist in a literary work is the character that is the protagonist's enemy; the character that the protagonist "struggles or contends with," or fights against (Wheeler, "Literary Vocabulary"). The antagonist can also be the source of conflict in the story. There are a couple of antagonists in the play; some are indirect, while only one is direct. The only direct antagonist in the play is actually Tybalt. When Tybalt sees Romeo at the Capulet's ball he feels insulted and vows revenge, as we see in his lines, "[T]his intrusion shall, / Now seeming sweet, convert to bitt'rest gall" (I.v.96-97). Tybalt's battle with Romeo of course leads to several deaths, Romeo's banishment, and eventually Romeo's own death. Hence, Tybalt is the only character that Romeo directly struggles against. However, the feud created by both Romeo's own family and the Capulets is also responsible for the conflict in the story, the separation of Romeo's and Juliet's love. In fact, had the feud not existed, Tybalt would never have felt insulted by Romeo's presence and never wanted to kill Romeo. Therefore, other indirect antagonists in the story are Lords Capulet and Montague.