Haikus
Haikus are the style of poetry strongly connected back to Japan, especially concerning the ephemeral nature of things depicted in many famous works. In the early days of the craft, the structure was looser, being composed of two parts that could be 5 and 12 syllables long, 12 and 5, 8 and 9, 9 and 8, 7 and 10, 10 and 7, or whatever length the poet felt appropriate for the piece. For an example of this, let's see a sampling of works from Basho, Issa and Buson(each accompanied by a rough translation)
行(ゆ)く春(はる)や
鳥（とり）泣（な）き、魚（うお）の目（め）に涙（なみだ）
The spring passes
The birds weep, tears in the eyes of fishes
-Basho
猫（ねこ）の飯（めし）相伴（しょうばん）するや
雀（すずめ）の子（こ）
Share a meal of rice with a cat
Does a baby sparrow
-Issa
我（われ）と来（き）て遊（あそ）べや
親（おや）のない雀
Come along and play with me, won't you?
You parentless sparrow, you
-Issa
鶯（うぐいす）の泣くや
小（ちい）さき口（くち）空（あ）けて
The bush warbler's warble away
Their small mouths opening so wide-Buson
In time, the structure around Haiku became stronger and formed into the 3 part, 5-7-5 form signature to it. Nature often inspires many classic Haiku, but they aren't always as serious or intense as folks would have you believe. In some instances, poets of the form are quite easy breesy about the kinds of Haiku they write, as shown by Yamazaki Sokan's poem detailing life in the sticks of Japan:
さ、お姫（ひめ）の
春、立（た）ちながら
尿（しと）をして
The Great Spring Goddess
Stands before all her subjects
And takes a nice whizz
我（わ）が親の
死（し）ぬる時（とき）にも
屁（へ）をこきて
Even as my dad
Drew in him his dying breath
He had cut the cheese
The 5 and 7 syllable style is also present in Tanka, which uses a 5-7-5-7-7 format for its works, as well as many other places in the country's history. For example, there's the line 「欲（ほ）しがりません。勝（か）つまでわ(We all shall want for nothing. Not 'til this is won)」, which was part of the propaganda of WWII Japan. The more you look at the country's proverbs, maxims, and song structures, the more these two styles will pop up, especially as they help guide the translation and adaptation of many foreign works brought into the country, such as in the phrase "All's well that ends well"(adapted as 終（お）わりよければ、全（すべ）てよし) and Auld Lang Syne, whose line "Should Auld acquaintance be forgot and never brought to mind" was translated to 「蛍（ほたる）の光（ひかり）、窓（まど）の雪（ゆき）」
-Keiko Imaoka(Forms in English Haiku)