If you want to form some random groups, take paper clips in various colours (depending on how many participants you want in one group, count them in advance and pick the appropiate number of different colours). Then, go around the circle and ask everyone to choose one paper clip from the pile in your hands (or a small box) followed by announcing that everyone with colour x will be in one group etc.
Fun fact: Came up with it on the fly when I forgot to prepare my groupings and all I had available was one of our boxes with stickies, pens and other material, including paper clips!