| These may not be forms, in the strictest form of the word, but definitions of sections, etc.. I will try and node the ones that aren't already there.
Before continuing on your journey, it may be good to read up on certain terms, like foot, meter, iambic (specifically iambic pentameter), stanza, rhyme, rhythm, metrical feet.
Here's the list:
Abstract Poem
Acrostic
Alexandrine
Allegory
Alphabet Poem
Alphenga
Aphorism
Astrorenga
Azenga
Babanga
Ballad
Ballade
Baraiasa
Blank Verse
Blues Poem
Bouts Rimés
Calligram
Canto
Canzone
Capriccienga
Carmen Figuratum
Catanga
Cento
Change
Cherita
Chrisenga
Cinquain
Clerihew
Collaboration
Colorengas
Concrete Poetry
Couplet
Crimenga
Diamonte
dodoitsu
Eclogue
Elegy
Elfchen
Englyn
Epic (see also mock epic)
Epigram
Epistle
Epitaph
Epithalamium
Essay
Event Poem
Exquisite Corpse
Found Poem (see also Found Poetry)
Free Verse
Garenga
Gembun
Ghazal
Gourmenga
Haiku (see Quaiku)
Haibun
Hasenfeffer Meatloaf
Higgledy-Piggledy
Hinky-Pinky
Historenga
Imitation
Insult Poem
Intimenga
Lantern
Light Verse
Limerick
List Poem
Literenga
Lorenga
Losenga
Luc-Bat
Lune
Lunenga
Lyric
Macaronic Verse
Madrigal
Maqamah
Marsiyeh
Maxim
Mesostic
Movierenga
Musaddas
Namenga
Narrative Poem
Nazm (see: masnavi, marsia, and qasida)
Ninenga
Nonsense Verse
Numenga
Occasional Poem
Ode
Octave
Omenenga
Orienenga
Ottava Rima
Palindrome
Pantoum
Parody
Pastoral Poem
Performance Poem
Phonenga
Placenga
Projective Verse
Prose Poem
Psalm
Quatrain
Rap
Rendango
Renga
Rengaccio
Rengatto
Ritual Poem
Rondeau
Satire
Sedoka
Senryu
Septenga
Sestet
Sestina
Skeltonic Verse
Soignenga
Sonenga
Song
Sonnet
Spirenga
Spoonerism
Sprenga
Stellarenga
Surrenga
Symbolenga
Syllabic Verse
Tanka
Tarji'-band
Tarkib-band
Tercet
Terse verse
Terza Rima
Thanatopsis
Triolet
Villanelle
Weddenga
Word Play
Yenga
These are by no means complete, /msg me with any additions. | 
