This quick and dirty angle grinder circle cutter certainly fills the bill ... powered up by a small 12-volt power supply, fixing the jig in place on the stock. The angle grinder is traced around ...
You can make a beam compass out or tie one end of a string to a nail and the other to a pencil, draw your circle, and cut freehand with a tool like a jigsaw or even (shudder) a handsaw.
A jigsaw can cut a circle of just about any size, from a little button to a large disc, not to mention other precise angles like triangles, squares, and more. So, the million-dollar question ...