For a bit of band saw fun check out this video by Adam Sandoval. While the cutawl used to be the closes thing to true 360 degree cutting, (and one of my favorite tools ever)the Rotozip spiral saw really carved a new direction for sawing. While it can not achieve the tight square corners that a scroll saw or a cutawl can, it can cut in any direction. While I suppose that you could achieve this with cnc routers and hand routers, the spiral bit makes it more appropriate.
Bestway Bandsaw Blades have adapted that technology to bandsaw blades, enabling spectacular cuts such as what is in the video. If you have another favorite supplier of blades that will cut 360 degrees, please chime in in let us know!
And in case your up to a little more fun with the bandsaw check out this project.