Below is a list of some of my favorite finds you might not have heard of yet.
A poem than uses repetitive lines to form a chant. (More methodical than a refrain. It is often repeated every line or every other line.)
Echo and Loop
A poem where the last word or syllable in a line is repeated or echoed underneath in the next line. If you restrict it to a 4-lined stanza and make the rhyme scheme abcb, it is called a loop poem.
A poem that’s created by erasing portions of an existing poem/story/speech (variation of a found poem).
A 6-lined poem with the following syllable count (1,1, 2, 3, 5, 8).
A 13-syllable poem that has 5 syllables in the first line, 3 syllables in the second line and 5 syllable in the final line. A variation of the poem uses words instead of syllables (3, 5, 3).
A poem where the end words of each line rhyme together.
A poem that can be read backwards and forward. (For Example: race car.) It can be done letter by letter, but also with words.
A 5-lined, thirty-one-syllable poem broken down into the following pattern: 5, 7, 5, 7, 7. Note: This form started out as a single line of poetry, so you can write it that way as well. Also, if you combine two tankas (like two letters talking to each other), then it is called a somonka.
A group of tercets united by using the second line to rhyme with the first and third lines of the following tercet so the rhyme scheme looks like: aba, bcb, cdc, ded, etc.
For examples and even more styles, you can check out the following sites: poets.org, poetryfoundation.org, shadowpoetry.com, writersdigest.com (http://www.writersdigest.com/whats-new/list-of-50-poetic-forms-for-poets), etc. Enjoy!