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If a poet was idealistic enough, or confused enough, or even fortunate enough, to have gone to college to study poetry, he or she would have certainly had at least one semester of Formal Verse. Writing poems in Formal Verse, be it cinquain, quatrain, haiku, sestina, or the venerable sonnet, is an exercise often overlooked by autodidactic poets. One may find it confining, confounding, even confusing in some cases, but it is a proven method for mastering meter and rhythm. Poets can then bring these elements into their Free Verse and create their own stanzas and patterns to fit each particular poem.
Below are a couple of reference pages with examples of Poetic Forms.
However, new forms are being invented and created all the time so no one list will be complete. Poetic Asides, the blog of Robert Brewer from Writer's Digest, actively encourages the creation of new forms so check them out too.
The 2/4/14 CUP meeting is designated for discussion on Forms. Information can be found here