Form, in poetry, can be understood as the physical structure of the poem: the length of the lines, their rhythms, their system of rhymes and repetition. In this sense, it is normally reserved for the type of poem where these features have been shaped into a pattern, especially a familiar pattern.
Another sense of "form" is to refer to these familiar patterns - these can be simple and open-ended forms, such as blank verse, or can be a complex system of rhymes, rhythms and repeated lines within a fixed number of lines, as a sonnet or villanelle is. (This is similar to the word "shape"; asked to think about "a shape", you would expect a triangle or a circle, but Alaska too has a shape.) The difference is visible in Sebastian Barker's poem 'Holy The Heart On Which We Hang Our Hope': the form of this poem shares aspects with another form, the villanelle, but also differs from it in interesting ways, just as its content shares in some aspects of organised faith but not in others.
This glossary includes full definitions of the most usual forms (sonnet, sestina, villanelle, blank verse...), with others below; poets will also invent their own forms, as in James Fenton's 'Jerusalem'.
An acrostic poem is one that uses the first letters of each line to spell out a word or phrase. More uncommonly, you can find a word or phrase through the centre of a poem (when it is called a mesostich) or at the end of the lines (which makes it a telestich). If the poem is written so that the first letters and last letters both write out a message, it is known as a double acrostic.
A poem consisting only of lines from other poems. This, from the Italian word for patchwork, is almost a technique rather than a form, especially as it can be of any length, and any metre, and need not rhyme; however, as the finished poem is referred to as a cento, just as a sonnet is called a sonnet, it is a form.
Named after its inventor, this is a four-line poem rhymed aabb; its first line is the name of the subject of the poem, it often breaks into two sentences at the end of the second line, and the rhythm tends to be entertainingly irregular.
This one is normally reserved for nonsense verse. 8 lines, all consisting of two dactyls (hence the name). Line 1 is a nonsense word (such as "higgledy-piggledy"), line 2 is someone's name, line 6 is a single six-syllable word, and lines 4 and 8 rhyme.
A stanza form often used for longer poems, most famously in Byron's 'Don Juan', consisting of eight lines, usually in iambic pentameter, rhymed abababcc.
This can be of any length; it is a poem of four-line stanzas, in which the second and fourth lines of one stanza become the first and third of the next. The last stanza's second and fourth lines can be the first and third of the first stanza, either reversed or not, which locks the poem into a circle of repetitions or, as the poet Marilyn Hacker says, "until it ends up with its tail in its mouth".
8 lines of iambic pentameter, followed by 1 iambic hexameter (or alexandrine); rhyme scheme ababbcbccc. This is the stanza invented by Spenser in The Faerie Queene.
A poem in which each stanza is rhymed aba, with the inner rhyme from one stanza providing the outer rhymes for either the previous or subsequent stanza: aba bcb cdc... or aba cac dcd.... The form can end in a single-line stanza, a couplet, or by referring back to the as-yet-unused rhyme from the first stanza.