One of the most popular poetry forms, because of its brevity, is the haiku. Consisting of three lines, this form is broken down into the number of syllables per line:
By the ancient pond 
When a frog leaps into it 
The sound of water 
This poem by Matsuo Basho focuses on the external. It doesn’t often stray into internal emotions, but focuses on the physical world, which is common to haiku.
Here are 5 other forms of waka poetry.
Our life in this world
To what shall I compare it?
It is like a boat
Rowing out at break of day
Leaving not a trace behind
– Priest Sami Mansei, translated by Steven D. Carter
Another popular form of waka, the tanka is slightly longer than a haiku. Another version of the tanka, called a renga, was popular from the 10th to 17th centuries. This form was written by two people. It consisted of a haiku, or hokku, written by one individual, followed by two lines that were written by another other. The renga was a collaborative form.
Shadow of moonlight
The breeze travels with her hair
Hearing her voice on the bank
A katauta is similar to a haiku despite the longer line at the end, although it is considered a “fragment” as compared to the other waka forms.
Sedoka (5-7-7 -5-7-7)
The sedoka is sometimes a dialogue poem, or mondoka, possibly between two lovers.
Choka (5-7-5-7-5-7…. 5-7-7)
Sources: Wikipedia, Poetic Meter and Form, World Poetry