Blank Verse is any verse comprised of unrhymed lines all in the same meter, usually iambic pentameter
Couplets
Short Couplet- iambic or trochaic tetrameter.
Split Couplet- the first line in iambic pentameter, the second in iambic diameter.
Heroic Couplet- two lines of iambic pentameter, also the last two lines of the English sonnet.
Alexandrine Couplet- an alexandrine is a line of iambic hexameter, so an alexandrine couplet is two rhymed lines of such.
Qasida is an Arabic form consisting of any number of lines all rhyming on the same rhyme.
Tercets are any three lines of poetry, whether as a stanza or as a poem, rhymed or unrhymed, metered or unmetered. The haiku is a tercet poem.
Quatrains are four line stanzas of any kind, rhymed, metered, or otherwise.
Sonnets were first written in Italian and were traditionally love poems. Though the sonnet is a form that can be experimented with, it has remained true to its original length of fourteen lines and its Anglicized meter of iambic pentameter.
Villanelles are a nightmare; there is no other way to say it. The form is originally French and didn't appear in English until the later 1800's. It is 19 lines long, but only uses two rhymes, while also repeating two lines throughout the poem.
Elements
Line and Meter
The line is the "bottom line." The sine qua non. If you ain't got line, you ain't got that swing. Swing being POETRY. Or at least verse.
Verse is cadenced language cut up into lines, and poetry is profound verse -- verse with layered multi-meanings as well as accumulated mega-meanings.
One of the differences between the modes of prose and verse is that the first doesn't break into lines and the second does. And that's a pretty profound thing in itself.
Rhyme and Music
Alliteration is only one of several ways to produce "music" in poetry.
Imagery is an artificial imitation of reality.
Form (that kind of encompasses everything we are talking about)
Tradition
All poets are talking to all past, present, and future poets.
All poems are talking to all past, present, and future poems.
Repetition
Repetition, however, is perhaps the most basic idea in poetics. There are all sorts of repetition: the repetition of rhythmic elements (meter); the repetition of sounds (rhyme, etc.); the repetition of syntactic elements (often a lineation device in open form); the repetition of stanzas (terza rima, for example), and so on.
Style
Style refers to the distinctive and idiosyncratic way one expresses oneself.