To behave impulsively is to act upon or to be swayed by emotions rather than by reason. Since uncontrolled, passionate emotions vs. rational thought is a dominant theme in Romeo and Juliet, there are certainly many instances in which both Romeo and Juliet act impulsively.
One example of Romeo acting impulsively can be seen when he allows himself to be swayed into crashing the Capulets' ball with Benvolio. Romeo is very hesitant to go, even believing that it is unwise and will lead to danger. He even relays a dream he had that he considers to be prophetic, and the dream reveals that the "night's revels" will lead to some horrible "consequence," even to his own "untimely death" (I.iv.114-18). Therefore, the fact that he allows himself to be persuaded into crashing the ball even though his reason is against it, shows us that he is allowing himself to be swayed by his emotions and his friends' emotions, rather than by reason. Since Romeo is allowing himself to be persuaded by his emotions, he is also acting impulsively.
Another example out of the many of Romeo acting impulsively can be seen with respect to his response to Tybalt slaying Mercutio. Romeo's rational senses would have told him to flee the scene. Tybalt fled the scene immediately after killing Mercutio but then comes back. Romeo would have been wise to flee also; instead, he decides to avenge himself on Tybalt for Mercutio's death. However Romeo's revenge is unnecessary as he knew full well that Tybalt would have been put to death by the law for having killed Mercutio. Had Romeo allowed the justice of the law to avenge Mercutio's death, he would have spared his own life as well as Juliet's. Yet Romeo allows himself to be ruled by his emotions rather than by his rational self, thereby acting impulsively.
Juliet is especially seen to be guilty of acting impulsively when she allows Romeo to persuade her into a rash and hasty marriage. Juliet had her hesitations from the start and saw that making a vow of commitment so soon was a rash and foolish thing to do, as we see in her lines:
Although I joy in thee,
I have no joy in this contract to-night.
It is too rash, too unadvis'd, too sudden. (II.ii.122-24)
Yet by the end of this scene she has allowed Romeo to persuade her to marry him the very next day. Juliet was using her reason when she felt her hesitations; however, by the end of the scene she lets her emotions govern her actions and, thus, acts impulsively.
There are quite a few instances in which Romeo and Juliet act impulsively. One of the very first is when Romeo first meets Juliet and professes his love for her without even knowing her name. He seeks her out at her balcony and insists on marriage within the next 24 hours. Juliet agrees and the Friar marries the two young children. However, these two have barely known each other for a day and are already engaged to be married. One could possibly say that their love for one another was not true but based on lust. Other examples include Romeo killing Tybalt and then taking a potion to kill himself at Juliet's tomb. If these two had thought about their decisions and the effects that they could have, there would have been a much different ending.