"Drama Activities for the Classroom and Beyond" lists a number of fun icebreakers and improv games for individuals and groups, alike. An added bonus is the Classroom Improvisation Guidelines link at the beginning of the article to help you effectively lead your troupe.
I have used tableau, a frozen picture or scene made by a group of people when teaching Arthur Miller's Death of a Salesman and August Wilson's Fences, but the activity can work with any text. Working in small groups, students have an opportunity to examine a text more closely and gain a deeper understanding as a result. Tableau is a fun activity to get students moving and collaborating as they figure out how to convey an important seen in a text using their bodies and their facial expressions.
Drama teacher, Stephen Wei, views his improv activities as a way to explore, "the intrinsic human truth that we bring into every drama." He also believes improv teaches students how to respect one another and to take risks. His students learn the value in teamwork, as well as the value in failure and learning from their mistakes.
This resource lists ways to utilize drama activities in every type of classroom from Art to Science to Math. DramaResource.com is a great resource, overall, for activities and lesson plans to help you integrate drama into the classroom.