There are over 51 types of poetry. Poetry is categorized by the number of lines in the poem, the words in the poem, whether it rhymes or not, and what it is about. Some types of poetry examples include haiku, free verse, sonnets, and name poems, although there are many more types as well.

• Haikus are one category of poems. The haiku originated from Japan, It’s the shortest type of poem and, often, the most difficult to understand. It consists of three lines that generally do not rhyme. The lines should have five, seven, and five syllables in them.
• Free verse poems are another type of poetry. A free verse is the loosest type of poem. It can consist of as many lines as the writer wants. It can either rhyme or not, and it does not require any fixed metrical pattern. Free verse is commonly used among writers because it allows for maximum flexibility.
• Sonnets are another classification of poetry. A sonnet is best described as a lyric poem that consists of fourteen lines. Sonnet’s have at least one or two conventional rhyme schemes. Shakespeare in particular was famous for writing sonnets.

• Name poems are popular among children and are often used in schools. The name of the person becomes the poem. Each letter in the name is the first letter in the line of the poem.
• Source: http://www.yourdictionary.com/grammar/examples/types-of-poetry-examples.html