Three Poem Styles.

Style one: Free verse poems.
A poem completely free, doesn't have to rhym but can if you want it too.
http://www.famous-poems.biz/Dylan_Thomas/Dylan-Thomas-poems-biography-collection-of-poetry.html
A writer of free poems is Walt Whitman, know to be the first free poem in english, although possible one came up in 1665.
http://www.boloji.com/poetry/learningzone/pkz11.htm

Style two: Elegy poems.
Poems that are usually dark, sad, and usually based off the death of a person.
http://www.famous-poems.biz/Dylan_Thomas/Dylan-Thomas-poems-biography-collection-of-poetry.html
a writer of this poem style is Kenneth.
http://www.poetryfoundation.org/archive/tool.poem.glossary.1.html?id=16
made from classical Greek and Roman literature, mostly composed of couplets.
http://www.prose-n-poetry.com/display_work/7482

Style three: Bio Poems
a poem written about yourself, anything about you, plans thoughts desires etc.
http://www.famous-poems.biz/Dylan_Thomas/Dylan-Thomas-poems-biography-collection-of-poetry.html
usually look like this,:
Line 1: Your character’s first name
Line 2: Four words that describe your character
Line 3: Brother or sister of...
Line 4: Lover of...(three ideas or people)
Line 5: Who feels...(three ideas)
Line 6: Who needs...(three ideas)
Line 7: Who gives...(three ideas)
Line 8: Who fears...(three ideas)
Line 9: Who would like to see...
Line 10: Resident of
Line 11: His or her last name
http://www.studyguide.org/bio_poem.htm
The first recorded is on march 1, 1885, by Frances Hawk.
Dylan Thomas writes them aswel.
http://www.famous-poems.biz/Dylan_Thomas/Dylan-Thomas-poems-biography-collection-of-poetry.html