While British-American poet W. H. Auden once described poetry as nothing more than memorable speech, there are a number of ways we can classify such speech to make it more recognisable and meaningful.
There are three broad categories that we can use to classify poems: epic, narrative and verse.
An epic is a long narrative poem that explores a serious subject.
Traditionally, epics followed the exploits of extraordinary individuals and involved some kind of supernatural forces. Examples of epics include The Epic of Gilgamesh, Homer's The Iliad and The Odyssey, and the Indian classics the Mahabharata and Ramayana.
In Europe in the Medieval period, epic poems explored Christianity and the Bible, as seen in Dante's Divine Comedy and Milton's Paradise Lost. Later epics in the Romantic and Modern eras focused more on humanity and human society, such as Wordsworth's Prelude and T.S. Elliot's The Wasteland.
Nowadays, there are comparatively few epic poems composed—perhaps an opportunity for an aspiring poet?
Dramatic poetry refers to plays that are written in verse. These plays are composed by playwrights and performed by actors on stage before an audience.
In the Classical Era, dramatic verse was found in Greek tragedies such as Sophocles' Antigone and Euripides' The Bacchae. Dramatic verse was also extremely popular during the Renaissance with Shakespeare its most well-known playwright.
Again, there are not many plays written in dramatic verse these days—perhaps another opportunity for an aspiring playwright?
William Shakespeare, the most well-known Renaissance playwright. 1800-50. Martin Droeshout the Younger. Metropolitan Museum of Art. Creative Commons
When we think of a poem we are thinking of a lyric, which refers to a short verse in the voice of a single speaker.
There are many different forms of lyrical poetry—some of the most famous being sonnet, quatrain and haiku. In addition, most songs are written in lyrical verse with musical accompaniment (the words in a song are still known as the lyrics).
Closer to the original form of lyrical verse are rap songs, which rely more on language and less on music. Slam poetry is also a popular underground form of lyrical verse.