There was a popular song in the late sixties by a female singer in which she asks her paramour if he is a Romeo or a Heathcliff. In her song, Romeo means the romantic lover, while Heathcliff--an allusion to the character in Charolotte Bronte's Wuthering Heights--is the brooding lover. Of course, the singer uses these two male characters as prototypes.
So, the pervading opinion of many about Romeo is that he is emotional, even overly emotional. As such, he does tend to become less than rational. Certainly, it is his emotional personality that leads him to act as impulsively as he often does. Here are some instances of his emotional behavior which prohibits his use of reason:
---After first meeting Juliet, Romeo falls hopelessly in love, climbs the fence to her orchard, drops in where a member of the Capulet household could easily have killed him, but thinks that he is on"love's light wings"(II,ii,30). When she steps out onto the balcony, he tells Juliet that he would rather die than be without her love:
And but thou love me, let them find me her:/My life were better ended by their hate,/than death prorogued, wanting of thy love. (II,ii,80-83)
--Another instance involves Romeo's Elizabethan superstition of the dark and of evil occurrences during the dark of night:
O blessed, blessed night! I am afeard./Being in night, all this is but a dream,/Too flattering-sweet to be substantial. (II,ii,145-147)
then after wooing Juliet, he rushes to Friar Laurence, and asks the priest to marry them:
Then plainly know my heart's dear love is set/On the fair daughter of rich Capulet./As mine on hers, so hers is set on mine,...We met, we wooed and made exchange of vow,/I'll tell thee as we pass; but this I pray,/That thou consent to marry us today. (II,iii,51-58)
Of course, Friar Laurence is shocked since he knows that Romeo has earlier claimed undying love for Rosaline. In fact, he comments on Romeo's irrationality:
Young men's love then lies/Not truly in their hearts, but in their eyes.(II,iii,61-62)
---During the confrontation between Mercutio and Tybalt, Romeo unwisely puts himself between the two. This was a most unreasonable action since he could have been slain by either one as their tempers were soaring. Also, he does not think of how he endangers Mercutio.
--At the news of his banishment, Romeo loses all reason and conflicts with Friar Laurence:
Yet 'banished? Hang up philosophy!/Unless philosophy can make a Juliet. (III,iii,58-59)
To this, Friar Laurence replies, "O, then I see that madmen have no ears," and Romeo retorts, "How should they, when that wise men have not eyes?" (III,iii,63)
---After the Nurse arrives at the cell of Friar Laurence, Romeo wants to kill himself:
O tell me, Friar, tell me,/In what vile part of this anatomy/Doth my name lodge? tell me, that I may sack/The hateful mansion. (III,iii,110-113)
(After these lines, Friar Laurence tries to reason with Romeo.)
---Certainly, in Romeo's references to Fate, he is irrational: He cries, "O, I am fortune's fool!" after learning of the decree of the Prince that anyone of the two families will be banished (III,i,136), and "Then, I defy thee, stars!" (V,i,24); after Balthasar tells him that Juliet's body "sleeps in Capels' monument."
---In the tomb of Juliet, Romeo does not try to ascertain why Juliet's body is still warm when he supposes that she is dead because of the news brought to him by Balthasar that he [the servant] saw that Juliet was dead a day ago.
In a way, this whole play shows Romeo being irrational.
You can see him being irrational about Rosaline right at the beginning of the play. He is being all gloomy just because she doesn't love him.
Then you see him falling for Juliet right away -- at first sight. Then you see him learning that she is a Capulet and still staying in love with her.
Later on in the play, you see him falling on the ground and throwing a tantrum (more of a my life sucks tantrum than an I'm angry tantrum) when he is going to be exiled.
So all in all he seems pretty irrational a lot of the time. But love is completely irrational, isn't it?