What are some quotes that show Romeo being impulsive in Romeo and Juliet?

Romeo impulsively moves from being the courtly lover to becoming the impetuous, impulsive lover and fighter, and then the depressed lover.

Act I

Early in the play Romeo reacts emotionally to the news that his beloved Rosaline is going to a convent as he speaks dramatically in oxymorons: "O heavy lightness! serious vanity!" (1.1.168). But in a few scenes, he is excited again, and becomes instantly in love at his first sight of Juliet:

Oh, she doth teach the torches to burn bright!
It seems she hangs upon the cheek of night
Like  a rich jewel in an Ehiop's ear--
Beauty too rich for use, for earth too dear! (1.5.43-45)

After seeing Juliet at the Capulet masque, Romeo rushes toward her when he finds a chance to speak with her, recklessly disregarding the fact that she is of the opposing family: 

If I profane with my unworthiest hand
This holy shrine,... (1.5.87-88) 

and he even boldly asks to kiss her:

Then move not while my prayer's effect I take.
Thus from my lips by thine my sin is purged. (1.5. 102-103)

Act II

After his passionate meeting with Juliet, Romeo rushes in the night to be able to see her, and, perhaps, again speak with her. Risking death if the Capulet guards see him, he scales the wall of the orchard and stands beneath her balcony. And, when Juliet comes out and speaks about Romeo and his name being their only impediment, Romeo boldly and impetuously declares that he will gladly change his name for her:

I take thee at thy word.
Call me but love, and I'll be new baptized.
Henceforth I never will be Romeo. (2.2.50-51)

Then, after exchanging their vows of love for one another, Romeo rushes to Friar Lawrence to ask him to perform the marriage ceremony for Juliet and him. Although the priest warns Romeo about being so impulsive--"These violent delights have violent ends" (2.6.7)--he feels that marrying the two may help to end the feuding of the two families. So, after knowing each other for only hours, Romeo and Juliet are married.

Act III

When Romeo finds his friends Benvolio and Mercutio engaged in a heated exchange with Tybalt, he rushes to stop the aggression between Mercutio and Tybalt. Unfortunately, he rashly thinks that his words of good will can soothe Tybalt, even though Tybalt has no knowledge of any change having taken place in this Montague. Unfortunately, Mercutio is stabbed because Romeo impulsively steps in the way, preventing Mercutio's sword from defending him.
Rashly discarding his good will after Mercutio dies, Romeo attacks Tybalt, crying out: 

Away to Heaven, respective lenity,
And fire-eyed fury be my conduct now!
Now, Tybalt, take the "villain" back again (3.1.85-87)

In his frenzy, Romeo kills Tybalt, an impetuous act which causes his banishment from Verona. 

Act V

When Romeo is misinformed by Balthasar that Juliet is dead, he rushes to an apothecary, demanding poison. Because the apothecary is poor, he gives Romeo the poison he wants. Then, Romeo hurries to the Capulet catacombs. Shortly thereafter, he encounters Paris, "Wilt thou provoke me? Then have at thee"(5.3.70), and he kills the count.

Finally, when Romeo discovers Juliet and believes her dead, he does not think things through at all. For, even though he notices that her face does not have the appearance of death--"Why art thou yet so fair?"(5.3.111)--he does not hesitate before he decides to join her in death. 

Amidst the whirlwind of his emotions, Romeo acts impulsively, thinking himself driven at times by Fate. But, more than his being "Fortune's fool," in his rash decisions and actions, Romeo himself seems to work against his own well-being and good fortune.