Jeff "Song Circles" vary quite a bit with the customs of the particular group. I assume we are talking about any group of people that get together on a more or less regular basis to sing (individually or collectively) that is not a featured performer versus audience arrangement. Let's not deify Rise Up Singing. Some groups use RUS or other books some of the time.

The groups I sing with mostly meet in people's houses with people sitting in a rough circle (depending on the furniture)taking turns leading the song. One of the groups often has theme for the night, the other doesn't. One group encourages singing/playing along more than the other, but there is some singing along in each.