How does "The Raven" by Edgar Allen Poe relate to Shakespeare's Romeo and Juliet and what are the similarities in their tragic events?

In both "The Raven" and Romeo and Juliet, a man must deal with the death of the woman he loves. In the poem, the unnamed narrator is mourning the loss of his lover, a woman called Lenore, who he describes as being with the angels now. In the play, Romeo learns of Juliet's death from a friend rather than from the friar, who knows the truth (that Juliet is not actually dead). In both texts, the men seem subject to some larger entity, haunted and taunted by something bigger than themselves. Romeo believes that he is "Fortune's fool," and the prologue refers to him and Juliet as "star-cross'd lovers." The night before he goes to the Capulets' party, he even says that he has some feeling that there is "Some consequence yet hanging in the stars" which will "bitterly begin his fearful date / With this night's revels . . ." Fate seems to be in control.
The narrator of the poem owns a bust of Pallas Athena, on which the raven initially perches, and he describes the raven as coming from the "Night's Plutonian Shore." Thus, he seems to espouse some level of belief in a higher power, something that he credits for the operations of life and death. He actually suggests that God might have sent the bird and even asks the raven if he will ever be reunited with Lenore in "the distant Aidenn," by which he seems to refer to heaven. The bird replies in the negative, and he continues to perch on the bust of Athena. Perhaps this narrator is crossed by the gods as Romeo is crossed by fate. In both texts, it seems as though they are not in control—something bigger is—and this something seems to care little, or not at all, for our tender feelings.

There are common themes of deep, obsessive love and unimaginable loss in the poem “The Raven” and the play Romeo and Juliet. They are both dark, brooding pieces.
The speaker in "the Raven" is a student who is visited by a talking raven one night. The bird reminds him of his sadness and isolation. He recently lost his great love, Lenore. He tries to get his mind off of it, but it is pointless.

Eagerly I wished the morrow;—vainly I had sought to borrow 
From my books surcease of sorrow—sorrow for the lost Lenore— 
For the rare and radiant maiden whom the angels name Lenore— 
Nameless here for evermore.

It is not entirely clear what happened to Lenore, but given the speaker’s misery and Poe’s past, it is likely she died.  She is lost to the speaker, causing him to be severely depressed. Losing Lenore might not be as dramatic as Romeo and Juliet’s demise, but I would argue the love story behind “The Raven” is every bit as meaningful as the one in the play. 
Romeo and Juliet’s deaths were caused by a family feud. They fell madly in love, but had to keep their love and marriage a secret. Then Romeo was banished because of a fight that occurred because of the feud. Juliet faked her death to avoid being forced to marry another man. Romeo does not know Juliet is not actually dead, and life without her seems so miserable that he takes poison and kills himself.

… O, hereWill I set up my everlasting rest,And shake the yoke of inauspicious starsFrom this world-wearied flesh. Eyes, look your last!Arms, take your last embrace! and, lips, O youThe doors of breath, seal with a righteous kissA dateless bargain to engrossing death! (Act V, Scene 3)

Juliet awakens to find Romeo has committed suicide. She then takes her dagger and kills herself. The two are so deeply in love that they cannot bear the thought of being apart. Like the speaker in "The Raven," love is everything to Romeo and Juliet. Its absence is unbearable. The difference is in the degree of their reactions; Romeo and Juliet kill themselves.