Haiku: Haiku is a traditional Japanese poetry form composed of 3 lines of 5, 7, and 5 syllables respectively. Actually, in Japanese they're usually written in one line, but still considered 3 separate units. Contemporary international haiku usually relaxes the syllable-count restriction. In English haiku, 1-3 lines of 17 syllables or less is the norm (14 syllables is often recommended). Haiku are poems about nature and generally follow the principles of minimalism and immediacy. Immediacy refers to the sense of a scene being directly presented to your senses. A haiku tries to capture a concrete image in place and time. A season word is usually required in the traditional form to place a poem in a specific season. A cutting word is also common to direct the flow of the poem.
Scifaiku: SciFaiku is a form derived from haiku with a science-fiction theme. Like haiku, SciFaiku poems stress minimalism and immediacy and are approximately 17 syllables or less. SciFaiku also frequently strives for insightful commentary on the human condition.
Tanka: Tanka are 5-line poems of 5, 7, 5, 7, and 7 syllables respectively. They are often composed of 2 parts: the 5-7-5 part and the 7-7 part, though this division varies. Unlike haiku, they are not generally restricted to nature or to the use of season words. The term "tanka" often refers strictly to modern poems in this form, whereas "waka" refers to pre-20th-century poems.
Waka: Like tanka, 5-7-5-7-7 syllable poems. "Waka" usually refers to pre-modern poems.
Renga: A renga is a series of linked poems of alternating 5-7-5 and 7-7 syllable stanzas. Renga is traditionally written collaboratively so that a group of writers alternates in writing each part. Renga stresses continual change. A renga never tells a story but instead is a series of stanzas where each stanza connects with its preceding stanza to form a meaningful unit, but no 3 stanzas in succession are intended to make sense. In fact, the emphasis is on adding a new stanza at each step which surprises in the way that it interprets the portion that immediately preceded it.
Rengay: A rengay is a modern 6-stanza form similar to renga, except that in contrast to a renga, a rengay is intended to deliberately carry a theme throughout, such as a common topic or a narrative. Rengay are intended to be collaborative -- with 2 authors (A and B), the number of lines for each stanza is A3 B2 A3 B3 A2 B3, where each successive stanza is written by an alternating author. With 3 authors, the sequence is A3 B2 C3 A2 B3 C2. Syllable count for each line is flexible, but 3-line stanzas are typically short-long-short (e.g. 5-7-5) and 2-line are typically long-long (e.g. 7-7).
Haikai-no-renga: "Haikai no renga" refers to a non-courtly form of renga, the kind that Basho wrote, a form of renga that stressed colloquial language, common experiences, and de-emphasized poetic flourishes. Haikai was often written for more humorous and less high-minded purposes, which allowed this form of renga a certain amount of vitality over the years.
Senryu: Senryu is structurally identical to haiku, that is, a 5-7-5 poem, but has a much more flexible content, in particular discussing human emotions and relationships as opposed to nature themes.
Haibun: Haibun is a prose form inspired by haiku. The form still stresses a certain conciseness of expression, but uses full prose sentences. It is used, for instance, for travel diaries, which include numerous references to natural scenes and contain good descriptive material. Haibun includes a number of haiku poems strewn throughout the text.
Haiga: Haiga is haiku-inspired art. Usually it is an illustration of a haiku with the haiku written on the picture. Haiga tends to be a fairly minimal style of painting.