You want to show interest in what the organization is doing. You want to demonstrate that you're eager to be a part of what's going on. You want the interviewer to begin to envision you as part of the team. And you really want to know more about what you'd be doing if you're hired. So a good question is, "What projects (or assignments) would I likely be involved in during my first few months on the job?" If your research -- or what's been said in the interview -- has made you aware of a specific project that interests you, you might ask if there's any chance that you'd be involved in that.
Keep reading for more helpful questions.