Here is a great exercise for a new group. The instructions are pretty simple. Go around the group giving each person the opportunity to choose one question and answer it honestly. Anyone can follow-up with an opinion or clarifying question (no critiquing each other's answers, though). Once a question has been answered, no one else may answer that question.
If your group is larger, you may want to alter the rule and allow each question to be answered 2 or 3 times. Ideally, each person should end up answering 3-5 questions.
As the leader, pay attention to the conversation. Let the discussion run its course as this is how people in the group build their relationships with one another. You can use these questions, modify them or create your own.