The conditions of Romeo and Juliet's relationship (situational irony)
Of all the people in the world that the offspring of sworn enemies Montague and Capulet could have fallen in love with, they had to fall for each other. Romeo and Juliet are described time and again as going against the stars, which were thought to be tied to destiny. Their entire relationship is an unexpected twist of fate, and is therefore the greatest overarching example of situational irony in the film.
Romeo doesn't know that Juliet's not really dead (dramatic irony)
Romeo not understanding that his wife isn't really dead despite the audience being made aware of it is a classic example of dramatic irony. We even know why he doesn't know: we see Friar Lawrence give Friar John the letter informing him, but then see that Balthasar reaches Romeo with the news of Juliet's "death" first, and the two boys ride right by Friar John without receiving his letter. This provides an additional point of tension, as the audience knows that Romeo doesn't have to die but is unable to do anything about it, as opposed to if they believed along with him that Juliet really was dead and didn't feel as conflicted about his decision to take his own life.
Juliet's fake death leads to her real one (situational irony)
Despite her threats to kill herself if she has to marry Paris, Juliet in effect tried to fake her death in order to avoid actually committing suicide. Nevertheless, when she unknowingly convinces Romeo to kill himself and awakens to see him dead, she is moved to the last resort of taking her own life, and so a fake death turns into a real one.
Mercutio's reputation as a joker prevents him from getting help (situational and dramatic irony)
Mercutio establishes himself from the get-go as the jokester of his group of friends, acting out funny characters and generally engaging in horseplay. As a result of this, when he's injured and hides his wound from his friends, they believe he's putting on an elaborate ruse for their amusement. Even as he insists that he legitimately needs help, his previous reputation as a perennial comedian discredits him and keeps them laughing. Only once he is dead on the ground and Romeo reveals his bleeding chest do they finally understand that this was no laughing matter.
