It may sound hokey, but there's something about a campfire that lends itself to singing! Take something that can be passed around. It can be anything--a funny-shaped stone, a stick, even a bag of marshmallows. Pass it around the campfire. Whoever has it is required to lead a song, something where they sing the verses and everybody joins in on the chorus. If it's a song that includes clapping, sound effects, or hand motions, so much the better.
If you don't know a song, I guess you'll just have to make one up!