What are the character traits of Romeo in Romeo and Juliet? Provide textual evidence.

In Shakespeare's tragedy Romeo and Juliet, Romeo goes on an emotional journey from a shallow, irresponsible, love-struck teenager to a more mature, deeply passionate, and compassionate young man.
Romeo is ordinarily level-headed, thoughtful, and relatively mature (for a teenager), as evidenced in his attempt to reason with Tybalt to avoid fighting him.

ROMEO: Tybalt, the reason that I have to love theeDoth much excuse the appertaining rageTo such a greeting. Villain am I none.Therefore farewell. I see thou knowest me not.
TYBALT: Boy, this shall not excuse the injuriesThat thou hast done me; therefore turn and draw.
ROMEO: I do protest I never injur'd thee,But love thee better than thou canst deviseTill thou shalt know the reason of my love;And so good Capulet, which name I tenderAs dearly as mine own, be satisfied. [3.1.61–71]

To mediate between the two hotheads, Tybalt and Mercutio, Romeo says the following:

ROMEO: Gentle Mercutio, put thy rapier up.
MERCUTIO: Come, sir, your passado!
They fight.
ROMEO: . . . Gentlemen, for shame! forbear this outrage!Tybalt, Mercutio, the Prince expressly hathForbid this bandying in Verona streets.Hold, Tybalt! Good Mercutio! [3.1.82–88]

Romeo also takes responsibility for Mercutio's death after his ill-advised and ill-timed intervention in Mercutio's sword-fight with Tybalt.

ROMEO: This gentleman, the Prince's near ally,My very friend, hath got this mortal hurtIn my behalf . . . [3.1.109–111]

Tomeo is deeply concerned about Juliet after his banishment, and when she learns that he killed Tybalt, he says,

ROMEO: Spakest thou of Juliet? How is it with her?Doth not she think me an old murderer,Now I have stain'd the childhood of our joyWith blood remov'd but little from her own?Where is she? and how doth she? and what saysMy conceal'd lady to our cancell'd love? [3.3.97–102]

Romeo is changeable, sometimes from moment to moment. At the start of the play, Romeo is lovesick for Rosaline.

ROMEO: The all-seeing sunNe'er saw her match since first the world begun. [1.2 96–97]

That is, right up until the moment he falls in love with Juliet at first sight:

ROMEO: O, she doth teach the torches to burn bright!Did my heart love till now? Forswear it, sight!For I ne'er saw true beauty till this night. [1.5.46–55]

Interestingly, Romeo's language takes on greater maturity after he meets Juliet.
Talking about Rosaline, Romeo's language is far more artificial and superficial than when he talks about Juliet, from expressions of utter rejection and over-the-top despair at his unrequited love for Rosaline...

ROMEO: Griefs of mine own lie heavy in my breast . . .Love is a smoke rais'd with the fume of sighs . . .Being purg'd, a fire sparkling in lovers’ eyes;Being vex'd, a sea nourish'd with lovers’ tears.What is it else? A madness most discreet,A choking gall, and a preserving sweet.Farewell, my coz. . . .She is too fair, too wise, wisely too fair,To merit bliss by making me despair.She hath forsworn to love, and in that vowDo I live dead that live to tell it now. [1.1 186-194, 223-226]

...To a more mature, more passionate—and more poetic—love for Juliet...

ROMEO: But soft! What light through yonder window breaks?It is the East, and Juliet is the sun!Arise, fair sun, and kill the envious moon,Who is already sick and pale with griefThat thou her maid art far more fair than she . . .Two of the fairest stars in all the heaven,Having some business, do entreat her eyesTo twinkle in their spheres till they return . . .The brightness of her cheek would shame those starsAs daylight doth a lamp; her eyes in heavenWould through the airy region stream so brightThat birds would sing and think it were not night . . .With love's light wings did I o'erperch these walls;For stony limits cannot hold love out,And what love can do, that dares love attempt. [2.2.2-6, 15–22, 70–72]

Romeo is impetuous. His impetuous and sometimes rash behavior is evident throughout the play, from the time he first trespasses on Capulet property to see Juliet to when he marries Juliet just one day after their first meeting. As he tells Friar Laurence,

ROMEO: Then plainly know my heart's dear love is setOn the fair daughter of rich Capulet;As mine on hers, so hers is set on mine,And all combin'd, save what thou must combineBy holy marriage. When, and where, and howWe met, we woo'd, and made exchange of vow,I'll tell thee as we pass; but this I pray,That thou consent to marry us to-day. [2.3.58–65]

Later, Romeo pulls his dagger and contemplates suicide when the Nurse tells him that Juliet is distraught because he killed Tybalt.

ROMEO: As if that name,Shot from the deadly level of a gun,Did murder her; as that name's cursed handMurdered her kinsman. O, tell me, friar, tell me,In what vile part of this anatomyDoth my name lodge? Tell me, that I may sackThe hateful mansion.Draws his dagger. [3.3.107–113]

He drinks a vial of poison when he mistakenly believes that Juliet is dead:

ROMEO: . . . Here's to my love! Drinks. O true apothecary!Thy drugs are quick. Thus with a kiss I die. [5.3.199–120]

Yet after fatally wounding Paris at Juliet's tomb, and even in the depths of his own grief in believing that Juliet is dead, Romeo compassionately fulfills Paris's dying wish.

PARIS: . . . If thou be merciful,Open the tomb, lay me with Juliet.Dies.
ROMEO: In faith, I will. . . .I'll bury thee in a triumphant grave. [5.3 72–83]