The list of writing exercises for poetry (and all genres really) is exhaustive. Here are some of the most successful:
Translation exercise: Bring in a poem in a language unfamiliar to your students. Without giving them any ideas about the poem's content, have them "translate" the poem by mimicking the lines and line integrity--the spacing of the poem. In terms of language, the students may do their best to divine subject matter and imagery. The result is a selection of poetry from students that is wildly different in focus, but which holds the original shape of the poem. When the exercise is completed, read the original out loud. Occasionally, students will happen upon the actual subject matter, so do not let that surprise you. A poem in German about a deer has yielded, for instance, five poems about deer in a class of 12. The object of the exercise is to examine pacing and tone.
Found poetry exercise: Find an old book and select a page of text. Write a poem using only the specific lexicon on that page. Some poets choose to mark out words with a marker, leaving behind words that form an unexpected poem. This exercise is particularly useful when discussing language, as so many of us call upon the same vocabulary over and over again. Borrowing language pushes writers outside of their own self-imposed limitations.
Photograph exercise: Hand out the same photograph (or image) that features at least two people to all students and have them write a poem based on the picture before them. Encourage varied approaches (first person point of view, dialogue, etc.), but limit the length. Restrict space to an index card or drawn square that is the same size as the photograph. Have students read their poems out loud, one after the other, with no commentary between poems. The idea behind the exercise is to encourage focusing on a particular image, voice or character.
First line exercise: Select a first line from a previously published work that appeals to you--the sentence can be one that is gripping or one that simply presents opportunity. Have students begin a short story using this common starting point. The idea is to take something small and specific and begin with that, as opposed to entering a story with more universal ideas in mind.
Fortune cookie exercise: This exercise requires a nominal purchase by the instructor, but bringing in fortune cookies for the class can produce surprising results. Once you have handed out the cookies, have them use the fortune inside as a first line for a story.
Second person exercise: Ask students to develop a short story told entirely from the second person point of view. Discuss the advantages, which include producing a sense of immediacy or urgency and intimacy with the reader born of the direct address form. Caution students against didactic, imperative sentences that may push readers firmly out of the story. The exercise is useful as it encourages writers to experiment with point of view; you could also, for example, assign them first person plural or third person limited.
Voice exercise: Students will pick a family member or close friend whose character fascinates them in some way. Have students begin an essay by doing a character sketch of this person. Suggest that they include traits unique to the person and passages of dialogue that showcase that person's voice.
First sound exercise: Have students work on the difficult task of teasing out early memories by focusing on the first sound they remember hearing. Afterward, ask students to begin an essay that both describes the memory and explores the significance of it. An entire essay can be constructed around memories of something specific, like sound. Often, writers will go regularly to the same memories for inspiration and neglect the small memories which can sometimes inform the entire character or crisis of the narrator.
House as character exercise: Tell students to begin an essay with a description of a house or room. The space should function as character and reveal something of the people who inhabit the space. Imagery should address all the senses and communicate the appropriate mood for the story.
There are many useful texts to help inform an instructor's methodology. "What If? Exercises for Fiction Writers," by co-authors Bernays and Painter, is now in its third edition. An extensive list of writing exercises as well as practical essays on the elements of fiction makes for a convenient resource.
The Association of Writing Programs (AWP) is both a website and a magazine to which creative writing teachers can subscribe. A good deal of information is available online regarding all genres and including exercises and articles on specific aspects of writing, teaching and publishing. AWP also hosts a writing convention once a year for which interested educators may sign up.
The Poetry Foundation home page has a great directory of articles, poet biographies, new poems and craft tools.