Even though theirs is a violent love, Romeo and Juliet are, indeed, truly in love because they risk their lives for this love, and they commit themselves to certain acts. Romantic love is the theme of Shakespeare's play.
Renowned psychologist Erich From writes in his book The Art of Loving,
To love somebody is not just a strong feeling--it is a decision, it is a judgment, it is a promise.
With Romeo and Juliet there is certainly erotic love, but there are also the acts of will requisite in a real love relationship. In Act I, Romeo and Juliet have clearly decided that they love each other and will commit themselves to this love. When Romeo sees Juliet, he realizes that he is in love by contrasting his feeling with those he had for Rosaline:
Did my heart love till now?....
For I ne'er saw true beauty till this night. (1.5.50-51)
Juliet, too, acknowledges to herself that she is in love after she is informed by the Nurse that Romeo is a Montague:
My only love sprung from my only hate!
Too early seen unknown, and known too late!
Prodigious birth of love it is to me,
That I must love a loathed enemy. (1.5.138-141)
In Act II, Scene 2, the famous balcony scene of dazzling imagery and exquisite poetic language, Romeo and Juliet promise each other their love and commitment. After Romeo speaks in terms of courtly love and metaphor, Juliet asks Romeo to tell her if he loves her--"pronounce it faithfully"--and she gives him her promise:
In truth, fair Montague, I am too fond [foolishly affectionate]
And therefore thou mayst think my 'havior light.
But trust me, gentleman, I'll prove more true
Than those that have more cunning to be strange
...I must confess....
My true love's passion..... (2.2.98-104)
Shortly after hearing Juliet's promise, Romeo makes his: "Lady, by yonder blessed moon I swear..." but Juliet begs him not to swear, so he asks for "The exchange of thy love's faithful vow for mine" (2.2.110,127).
In Act IV when Juliet is told by her parents that she must marry Paris, she decides that she cannot do this since she is already married to Romeo and she loves him. Then, she follows the advice of Friar Laurence and drinks from a vial to make her appear to be dead in order to afford the priest some time to reason with the Capulets and ameliorate the relationship between the two feuding families. However, the results of this plan become tragic because Romeo, upon finding her in the Capulet tomb, believes her to be truly dead, and he decides to kill himself. After she awakens too late to prevent this tragic act, she discovers her beloved Romeo and decides that she cannot live without him, slaying herself with a knife. Theirs is a fatal judgment, but it seems that Romeo and Juliet have truly loved one another.
Romeo and Juliet are truly in love. They are willing to die for one another. Romeo killed himself with poison because he thought Juliet was dead and couldn't bear the thought of living without her. When Juliet woke to find Romeo dead, she cried that he didn't leave her any poison so she could join him. So, she took his dagger, and stabbed herself. If Romeo would have waited a little longer before taking such drastic measures, however, Juliet and Romeo would have had a much better ending. Neither Romeo or Juliet could bear living without the other. So, in conclusion, they are very much in love.
While it may seem as puppy love since it is such a young age, however, their commitment towards one another is what separates their love from puppy love. Some may say they have been caught up in their feelings and believed they were "in love" when in reality they were not, yet by sacrificing their lives for each other, they prove how truly in love they were and why Romeo and Juliet is such a prominent love story.