There are many different types of poetry. I counted 50 on a quick search of the internet. You may have heard of Haiku and Limericks. There are the more obscure types too, like Terzanelle and Sestina. Learning different types of poetry though, isn't nearly as much fun as inventing your own, so here are some ideas about that.
Types Of Poetry - Playing With Stanzas
What is a stanza? A division of a poem consisting of two or more lines. How many ways can you structure a stanza? As many as you want. Look at this stanza from the poem, "Gratitude:"
So there is nothing to say
There is nothing to say
There is nothing
Nothing...
But gratitude
Each line is a smaller part of the previous line. In this case, it quiets the mind in order to emphasize the last word: gratitude. However, this idea could be used in many ways. You could start with a line like, "She watched the birds come in from the sea," and it can reduce to, "Come in from the sea;" "From the sea:" "Where Michael was left alone in the storm."

Each stanza could have lengthening lines. Lines could be varied in length to create a picture on the page. Playing with stanzas is a fun way to create new types of poetry.
Ideas For New Types Of Poetry
In the poem "Do Not Believe In God," each stanza starts with one of our senses: "See God... in stars and sunlight... and the face of your lover;" Hear God... in wind and waves... and the music of the birds." All the senses are covered. How could we use this general idea? By starting each stanza with a different verb or adjective? By starting each stanza with a different person's name? By having each stanza get smaller or larger as the poem progresses?
How many ways can you play with poems? "Dream poems," could be a type of poetry that puts actual dreams into verse. "Dialog poems" could have stanzas or lines answering each other back and forth. A series of poems could use all the exact same words, rearranged, with an entirely different outcome in each. There are endless types of poetry you can create.