I have seen Twitter incorporated into the classroom a few times. All of the times Twitter was successful in the classroom because students had a fun time "tweeting" to other students and also the teacher. I would incorporate Twitter into Social Studies and also Science. Students could research about a famous person or idea and "tweet" to each other on a class Twitter account.
Twitter exit cards -- Today's Teaching Tweet. Students put their names in the form of @____ and then below that they write what they learned from today's lesson. Lastly, they #hashtag a "trending topic."