Word Wool's Team 
Monody is a poem form inspired by the old Greek odes, and more specifically elegies. It is a poem of grieving, meant to be recited by a single person. As such, monodies do have a tendency to be more personal than other elegies, referencing the feelings of the individual rather than the general opinions of a group.
Allegorical poetry refers to any poem in which allegory is a major element, but when calling an entire poem an “allegorical poem” we would usually understand it to mean that the entire poem is an allegory. Specifically, this means it is a poem with a specific moral, political, or spiritual message as its main purpose.
Slam poetry is a type of competitive poetry that emerged after Marc Kelly Smith started holding competitions in the 1980s, coining the term “poetry slam” for these events. Slam poems are prepared with an emphasis on vocal delivery and audience engagement. They’re as much about the performance as the poem.
Gwawdodyn Hir is a Welsh meter based on sixains (six-line stanzas). It combines lines of nine and ten syllables, utilizing rhyme and cross-rhyme to enforce rhythm. Superficially, it is an expanded version of the Gwawdodyn Byr, taking that same form and adding two more lines to it.
Trian Rannaigechta Moire is an ancient Celtic poem form that prizes rhymes and consonance. The form is comprised entirely of quatrains that have an internal xABA rhyme structure, in which ‘B’ will correspond to a syllable in the middle of the last line if certain conditions are met.
Gwawdodyn Byr is a Welsh meter based on quatrains that is nearly, but not quite, isosyllabic. It features two nine-syllable lines followed by two ten-syllable lines, with a single rhyme sound that appears on all four lines. The sound appears at the end of lines one, two, and four, but in the middle of line three.
An Englyn is one of several types of short poems from Wales. They feature combinations of a ten-syllable line, a short line (five or six syllables), and one or more seven-syllable lines, along with rhymes. Sometimes the entire poem is isosyllabic, featuring only seven-syllable lines.
The Gwawdodyn verse form is the 20th of the codified Welsh meters. This form is made up of quatrains comprised of distinct couplet forms that are, themselves, other members of the codified meters. More specifically, a Gwawdodyn verse will be a Cyhydedd Naw Ban couplet followed by either a Toddaid or a Cyhydedd Hir.
An endecha is a type of Spanish dirge or song of lament originating from the 16th century. The form relies on rhymed quatrains, usually with an uneven structure centered on lines with seven and eleven syllables, though a variant does exist that uses isosyllabic six-syllable lines instead.
The décima espinela is a poem written in ten-line verses utilizing isosyllabic rhymed lines. This variant of the décima was invented by Vicente Espinela, whose name lives on in the name of the poem, much like how we refer to sonnets as ‘Shakespearean’ or ‘Petrarchan.’
Jintishi, or regulated verse, is a group of Chinese poem forms that rely heavily on tonality and rhyme, traditionally written in couplets. This particular form is so entrenched in tonality that there is no true English equivalent, since the English language has a limited relationship with tone compared to Chinese.
Rannaicheacht Mhor is an ancient Irish poem form based entirely on quatrains. The lines of the quatrain are isosyllabic, a relative rarity among Irish poem forms, and cross-rhymes are used liberally. In particular, every line includes a word that matches the end rhyme in its paired line.
Lethrannaegecht Mor is a casual form hailing from ancient Ireland. As with many Celtic forms, there is an emphasis on repeated sounds and rhyme. This particular form is fairly compact, with each verse being just twenty syllables, though the poem as a whole can be any number of verses.
Hir a Thoddaid (literally “long stanza with a Toddaid”) is the 22nd of the codified Welsh meters. It consists of an isosyllabic mono-rhymed quatrain followed by a Toddaid couplet, which is itself the 19th meter. This unique form is the most commonly used of the awdl forms in the modern day.
While you might hear that the gogyohka is a short Japanese poem form and mistakenly conflate it with the extremely popular haiku, the two are not related. The gogyohka is a modern invention of the Japanese poet Enta Kusakabe (born 1938) and only has two simple rules. It is five lines long. Each line is one phrase.
Masnavi (or mathnawi) are a poem form that emerged from the middle east, and most likely the Persian empire, sometime between the 4th and 10th century. The form is entirely comprised of couplets, though triplet variants exist, with isosyllabic lines of either ten or eleven syllables and varies from region to region.