There are quite a number of examples of alliteration throughout the poem. The most common is the alliteration of the s-sound. Poe starts off with alliteration in the first line:
Be silent in that solitude
Poe's repetition of the s-sound emphasizes his sadness, sorrow and his solitude. He also emphasizes the nature of the spirit world. It is a secret, silent and mysterious world, not entirely understood.
There is, however, a break from this depressing mood. In line three, stanza four, the reference to hope is given a lyrical quality through the alliteration of the l-sound:
With light like Hope to mortals given—
The lyrical 'l' emphasizes an escape from the pervasive darkness that the speaker is experiencing. There is enlightenment, an aspiration to betterment.
In stanza four, there is greater positivity. The speaker is more concrete in his thinking; this is illustrated by the alliteration of a harsher (but more concrete) 'th' sound:
Now are thoughts thou shalt not banish,
The line is written in the form of a command willing the reader (and the speaker) to remember the past. This is further accentuated by the alliteration of 'v' in the line immediately following:
Now are visions ne’er to vanish;
In the final stanza, Poe emphasizes the importance of being alive through alliteration of the 'b' sound. It is the breath of God that keeps us going.
The breeze—the breath of God—is still—
Finally, the alliteration of 'm' adds to the emphasis of the mystery life and death holds over us.
A mystery of mysteries!
It is inexplicable, and the use of the exclamation mark further accentuates the fact.