Types of Poem

Narrative poem:

A narrative poem  tells a story. It has a full storyline with all the features of a traditional story.  They are characters, plot, conflict and resolution, setting and action.  It is a metered poem with clear objectives to reach a specific audience. These poems have been borrowed from oral poetic narratives from different cultures. Narrative poems include old epics, lays and ballads.

Example : "The Raven" by Edgar Allen Poe
“Once upon a midnight dreary, while I pondered, weak and weary,

Over many a quaint and curious volume of forgotten lore—

While I nodded, nearly napping, suddenly there came a tapping,

As of some one gently rapping, rapping at my chamber door.

“’Tis some visitor,” I muttered, “tapping at my chamber door—

Only this and nothing more.”

This is a famous narrative poem by an American story writer and Poet, Edgar Allen Poe.  It tells about a Raven who visits a lamenting lover who laments for the loss of his beloved Lenore.  It starts like a short story with a supernatural atmosphere.  It has a proper Settings, action and character representations, and resolution of the conflict.

The function of the narrative poem is to give a solution with moral lesson at the end.  It is because it narrates a conflict between dark and light or good and evil.  The readers have to understand and capture the meaning of the end through their analysis and deep study of each character in the poem.

Another main purpose of the narrative poem is to creative a emotional national feeling to inspire the readers.  In certain situations the poem could become a national song and mesmerises the readers to persuade them cling to their cultural atmosphere.

Allegory:  A story,poem,or picture that can be interpreted to reveal a hidden meaning, typically a moral or political one.

example: George Orwell, Animal Farm.  Animal Far is a great example of allegory.
Pilgrim's Progress by John Bunyan is a spiritual Allegory.  It tells the story of a man's journey from the City of Destruction to the Celestial City, representative of the journey to Heaven.

Ballad: A poem or song  expressing a story in small or short stanzas.  Traditional Ballads are unknown having been passed orally from one generation to the next.

Example:  La Belle Dame sans Merci by John Keats.

Blank verse:   Unrhymed verse, especially the unrhymed iambic pentameter most frequently used in English dramatic, epic, and reflective verse. 

Example:  HAMLET: To be, or not to be- that is the question:
Whether ’tis nobler in the mind to suffer
The slings and arrows of outrageous fortune
Or to take arms against a sea of troubles,
And by opposing end them. To die- to sleep-
No more; and by a sleep to say we end
The heartache, and the thousand natural shocks
That flesh is heir to. ‘Tis a consummation
Devoutly to be wish’d. To die- to sleep.
To sleep- perchance to dream: ay, there’s the rub!

Elegy:  (in modern literature) a poem of serious reflection, typically a lament for the dead.
Example:  "O Captain! My Captain!" which was written in memory of Abraham Lincoln:

Epic:  A long poem, typically one derived from ancient oral tradition, narrating the deeds and adventures of heroic or legendary figures or the past history of a nation. Epic literature belongs to the narrative genre of poetry. A narrative poem will tell a story of societies and heroes. The subject matter includes topics of human interest. Ballads are narrative poems, as well as epics.  The Iliad and The Odyssey are two Greek poems written by Homer. The Iliad tells of the last year before the city of Troy was overrun by the Greeks. The Odyssey is about Odysseus and his return home to Ithaca.

Free verse: poetry that does not rhyme or have a regular rhythm.
Example:"Samson Agonistes" by John Milton

But patience is more oft the exercise

Of Saints, the trial of their fortitude,

Making them each his own Deliver,

And Victor over all

That tyranny or fortune can inflict.

Limerick: A humorous five-line poem with a rhyme scheme aabba.
example: Hickory dickory dock.
The mouse ran up the clock.
The clock struck one,
And down he run.
Hickory dickory dock.

Lyric: Lyric" comes from the Latin word "lyricus," meaning "of/for the lyre." These short poems were originally accompanied by music. So in lyric poetry, the mood is melodic and emotional. The writer uses words that express his or her state of mind, perceptions, and feelings, rather than tell a story. A lyric poem is usually written in the first person. 
Example:  "Sonnet Number 18:"  by William Shakespeare.

Ode:  A lyric poem, typically one in the form of an address to a particular subject, written in varied or irregular metre.A classical poem of a kind originally meant to be sung.
Example:  "Ode on a Grecian Urn" by John Keats, Other well-known odes include Percy Bysshe Shelley's "Ode to the West Wind," Robert Creeley's "America," Bernadette Mayer's "Ode on Periods," and Robert Lowell's "Quaker Graveyard in Nantucket."

Pastoral: The pastoral poem presents an idealistic, almost Utopian, view of rural life. In these poems, shepherds and shepherdesses are innocent, pure, and free from corruption of the city or even the court. Some common topics of these poems were death, love, the mockery of politics, and the ideal life of the country.
Example: Christopher Marlowe's poem, The Passionate Shepherd to His Love

Petrarchan Sonnet: A sonnet composed of a group of eight lines (octave) with two rhymes abba abba, and a group of six lines (sestet) with two or three rhymes variously arranged, typically cde cde or cdc dcd: the thought or theme is stated and developed in the octave, and expanded, contradicted, etc. in the sestet; Italian sonnet.
Example:William Shakespeare wrote many sonnets, and even used the form in many of his plays, such as the famous prologue to Romeo and Juliet.

Sonnet: A sonnet is a poetic form that has fourteen lines. It originated in Italy in the thirteenth century, and though it has generally kept some of the original rules, such as the number of lines and having a specific rhyme scheme and meter.