Here’s a list of poetry type by ethnicity/nationality.
These are described in excellent book Shapes of Our Singing by Robin Skelton. The purpose of this post is to support the fact that almost every culture has a rich tradition of poetics.
If you know of another form, please comment.
Anglo-Saxon
Alliterative verse a la Eduard Sievers
Hazaj
Mutaquarib
Qasidah in the Basit
Rajaz
Sari
Tawil
Urjuzah
Wafir
Payar
Tripadi
Octosyllabic couplets
Than-bauk
Ya-du
Tetrasyllabic couplets
Ch’I-yen-shih
Chueh-chu
Ssu-yen-shih
Wu-yen-shih
Adonics
Alcaics
Alcmanic
Amphribachic trimeter
Anacreontics
Anapaestic dimeter
Antispastic dimeter
Archilochean
Asclepiadean
Bacchiac
Bacchic
Choliambic
Choriambic dimeter
Cretic
Dactylic hexameter
Dactylo-Epitrite
Dochmiac dimeter
Elegiac couplet
Enoplius
Epitrite dimeter
Galliambs
Glyconic
Hemiepes
Hendecasyllabic
Iambelegus
Iambic trimeter
Ionic a majore
Ionic a minore
Ithyphallic
Paeon
Paroemiac
Penthemimer
Phalaecean
Pheracratean
Priapean
Prosodiakon
Reizianum
Rhopalic
Sapphic
Saturnian
Senarius
Skolion
Sotadeon
Telesillean
Trochaic tetrameter
Versus spondaicus
14th century stanza
Czech
14th century traditional couplet
English
Acrostic
Alexandrine couplet
Ballad
Blues stanza
Burns stanza
Carol
Cinquain
Common measure
Clerihew
Cumulating verse
Diminishing verse
Diminishing and cumulating verse
Disyllabics
Double dactyls
Echo verse
English quintet
Heroic couplet
Hudibrastic verse
In memoriam stanza
Limerick
Long measure
Madrigal
Palindrome
Madsong stanza
Poulter’s measure
Primer couplet
Rime Royal
Roundel
Roundelay
English rubai
Interlocking rubiyat
Short hymnal stanza
Short particular measure
Skeltonic
Caudate sonnet
Curtal sonnet
Shakespearean sonnet
Spenserian sonnet
Split couplet
Triversen
Trisyllabics
Tudor lyric
Ethiopian
Mawaddes
Finnish
Kalevala meter
French
Ballade
Double refrain ballade
Ballade supreme
Bref double
Chant royal
Dizain
Huitain
Kyrielle
Lai
Lai nouveau
Ronsard’s ode
Pantoum
Rondeau
Rondeau redouble
Rondel
Rondel supreme
Rondelet
Rondine
Spondaic triolet
Tautogram
Reverdie
Rimas dissolutas
Rime couee
Rime riche
Triolet
Villanelle
Virelai
German
Knittelvers
Nibelungen stanza
Shuttelreim
Hebrew
Abecedarius
Traditional
Hindi
Doha
Irish
Ae freslige
Breccbairdne
Casbairdne
Cethramtu rannaigechta Moire
Cro cumaisc etir casbairdni ocus lethrannaigecht
Dechnad cummaisc
Dechnadh mor
Deibide
Deibide baise fri toin
Deibide guilbnech
Deibide guilbnech dialtach
Droigneach
Lethrennaigecht mor
Rannaigecht
Rannaigecht bec
Rannaigecht mor
Rannaigecht mor gairit
Rinnard
Rinnard tri-nard
Seadna
Seadna mor
Snam suad
Sned-bairdne
Treochair
Trian Rannaigecht Moire
Italian
Canzone
Decima Italiana
Italian octave
Italian quatrain
Italian sestet
Ottava ima
Petrarchan sonnet
Rispetto
Sestina
Rhymed sestina
Sicilian octave
Sicilian quintet
Sicilian septet
Sicilian sestet
Sicilian sonnet
Sicilian tercet
Stornello
Strambotto
Terzanelle
Terza rima
Terza rima sonnet
Japanese
Choka
Dodoitsu
Haiku
Imayo
Iroha mojigusari
Katauta
Kouta
Mondo
Renga
Sedoka
Senryu
Somonka
Waka
Javanese
Kakawin stanza
Sardula-vikridata
Tengahan wokir
Kashmiri
Vakh
Korean
Kasa
Sijo
Latin
Goliardic
Latvian
Daina
Malay
Pantun
Marathi
Abhanga
Ovi
Mongolian
Traditional meter
Occitan
Dansa
Old Norse
Drottkvaett
Fornyroislag
Hrynhent
Kviouhattr
Ljooahattr
Malahattr
Runnhent
Persian
Persian
Hazaj
Mathnavi in the Mutaquarib
Mujtass
Ramal
Rubai
Prakrit
Arya
Russian
Dolnik
Onegin
Sanskrit
Anustubh
Drutavilambita
Indravajira/Upendravajira
Jakati
Sardula-vikridita
Tristubh
Spanish
Copla de Arte Mayor
Cueca Chilena
Cuaderna via
Endecha
Flamenca
Folia
Glose
Lira
Mote
Pregunta
Quintilla
Redondilla
Seguidilla
Sextilla
Soledad
Zejel
Sumerian
Sumerian stanza
Swahili
Muyaka stanza
Tamil
Aciriyappa
Kali meter
Venpa
Thai
Totok
Tibetan
Gzha
Vietnamese
Luc-bat
Welsh
Awdl Gywydd
Byr a Thoddaid
Clogyrnach
Cyhydded fer
Cyhydded hir
Cyhydded naw ban
Cyrch a Chwta
Cywydd Deuair Fyrion
Cywydd Deuair Hirion
Cywydd Llosgyrnog
Englyn Lledfbroest
Englyn Milwr
Englyn Penfyr
Englyn Proest Dalgron
Englyn Proest Gadwynog
Englyn Unodl Crwca
Englyn Unodl Union
Gwawdodyn
Gwawdodyn Byr
Gwawdodyn Hir
Hir a Thoddaid
Rhupunt
Tawddgyrch Cadwynog
Toddaid
Yiddish
Folk meter