The first mention of birds in Shakespeare's Romeo and Juliet occurs in act 1, scene 2. Romeo is lovesick over "the fair Rosaline," and Benvolio is trying to convince Romeo to go with him to the Capulet's feast, where Romeo will be able to view young ladies who Benvolio assures him are even more beautiful than Rosaline.

BENVOLIO. At this same ancient feast of Capulet's
Sups the fair Rosaline whom thou so lov'st;
With all the admired beauties of Verona.
Go thither, and with unattainted eye
Compare her face with some that I shall show,
And I will make thee think thy swan a crow. (act 1, scene 2, lines 86–91)

Romeo mentions crows again after he's seen Juliet at the Capulet's feast in act 1, scene 5 and compares her to a snowy white dove in the company of crows, in much the same way that Benvolio compared Rosaline to the other young women at the feast.

ROMEO. O, she doth teach the torches to burn bright!
It seems she hangs upon the cheek of night
Like a rich jewel in an Ethiop's ear—
Beauty too rich for use, for earth too dear!
So shows a snowy dove trooping with crows
As yonder lady o'er her fellows shows. (act 1, scene 5, lines 46–51)

Juliet repays the favorable comparison to Romeo in act 3, scene 2 while she waits for him on their wedding night.

JULIET. Come, night; come, Romeo; come, thou day in night;
For thou wilt lie upon the wings of night
Whiter than new snow upon a raven's back. (act 3, scene 2, lines 18–20)

In the same scene, however, Juliet's description of Romeo is considerably harsher when she hears from the Nurse that Romeo has killed Juliet's cousin Tybalt.

JULIET. O serpent heart, hid with a flow'ring face!
Did ever dragon keep so fair a cave?
Beautiful tyrant! fiend angelical!
Dove-feather'd raven! wolvish-ravening lamb! (act 3, scene 2, lines 76–79)

In this same scene, Juliet also makes reference to a "cockatrice" when she first believes that Romeo is dead.

JULIET. (to Nurse) What devil art thou that dost torment me thus?
This torture should be roar'd in dismal hell.
Hath Romeo slain himself? Say thou but "I,"
And that bare vowel "I" shall poison more
Than the death-darting eye of cockatrice. (act 3, scene 2, lines 46–50)

A cockatrice is a mythological creature with the head and feet of a rooster and the body of a dragon, whose glance can turn a person to stone.

In act 2, scene 4, Mercutio talks about a "wild-goose chase," and Mercutio and Romeo make several bad puns, equating "goose" with being a fool and a woman-chaser.

There are several mentions of larks and nightingales early in the morning after Romeo and Juliet's wedding night together.

Juliet tries to convince Romeo that he heard a nightingale, not a lark, even though she knows quite well it's not a nightingale.

JULIET. It was the nightingale, and not the lark,
That pierc'd the fearful hollow of thine ear.
Nightly she sings on yon pomegranate tree.
Believe me, love, it was the nightingale. (act 3, scene 5, lines 2–5)

Romeo reminds Juliet that he's been banished from Verona, and he'll be put to death if he's found in the city, but he acts as if he's willing to stay with Juliet and die, if that's what she really wants.

ROMEO. I'll say yon grey is not the morning's eye,
'Tis but the pale reflex of Cynthia's brow;
Nor that is not the lark whose notes do beat
The vaulty heaven so high above our heads.
I have more care to stay than will to go.
Come, death, and welcome! Juliet wills it so. (act 3, scene 5, lines 19–24)

Juliet quickly realizes the seriousness of the situation if Romeo stays, and she agrees that it's morning, and Romeo must leave her.

JULIET. It is the lark that sings so out of tune,
Straining harsh discords and unpleasing sharps.
Some say the lark makes sweet division;
This doth not so, for she divideth us.
(act 3, scene 5, lines 27–30)

Later in this same scene, Juliet's father demands that Juliet marry Paris, and the Nurse tries to convince Juliet to abandon Romeo and marry Paris by comparing the two young men.

NURSE. I think it best you married with the County.
O, he's a lovely gentleman!
Romeo's a dishclout to him. An eagle, madam,
Hath not so green, so quick, so fair an eye
As Paris hath.
(act 3, scene 5, lines 218–222)

Juliet isn't convinced, of course, but she agrees to marry Paris until she can arrange for Romeo to return to Verona and take her away with him to Mantua.

Birds of several kinds are mentioned throughout the play. They frequently represent the themes of dark and light or night versus day, as when Juliet says that when night falls, she wants Romeo to come to her “Whiter than new snow upon a raven’s back.” She is using the contradiction or opposite of the white snow versus the black raven to show the contradiction she feels about night versus day. Her meaning is that the world loves day more than night, but Romeo will make night the best time for her. Moreover, to emphasize her love for him, the entire world "will be in love with night" when they realize how wonderful Romeo is.

In addition, birds also represent freedom versus captivity or the lack of freedom to do what one wants, which is certainly how Romeo and Juliet feel about their relationship. For instance, in act 2, there are two examples where Juliet likens Romeo to a bird that she could keep captive. In one, she longs for “a falc’ner’s [or falconer’s] voice” to lure Romeo, presumably the falcon, back again.

Later when it is nearly morning and she knows Romeo must leave, she says that she wishes Romeo were “a wanton’s bird.” She would allow him to leave but then pluck him back again “Like a poor prisoner. ... So loving-jealous of his liberty.” Romeo agrees with Juliet, saying he wishes he were Juliet's bird so that he could be her prisoner—or more precisely, be with her always.

Juliet acknowledges that if Romeo were her bird, she would kill him “with much cherishing.” This reinforces the strength of her love for him and her wish to hold him, perhaps so tightly that it would ultimately harm him.

Birds, including doves, crows, falcons, ravens, nightingales, and larks flutter through the lines of Shakespeare's Romeo and Juliet. They are often used to reinforce Shakespeare's theme of light and dark. 

In Act I, Scene 5, when Romeo sees Juliet at Capulet's party, he suggests that her beauty lights up the room. He says she teaches the torches to burn bright and is so beautiful it is as if she is a dove in the company of crows. He says,

O, she doth teach the torches to burn bright!
It seems she hangs upon the cheek of night
As a rich jewel in an Ethiop’s ear—
Beauty too rich for use, for Earth too dear.
So shows a snowy dove trooping with crows
As yonder lady o’er her fellows shows.

The brightness of her cheek would shame those stars
As daylight doth a lamp; her eye in heaven
Would through the airy region stream so bright
That birds would sing and think it were not night.