This all started when I was thinking about my Ultimate Business Card and how I could make it. It's very very difficult and expensive to find a printing company that can cut and score products, so I was thinking about making a custom die punch. I searched, and found out there are computer-controlled machines for home use that do a similar thing.
The problem with searching for these devices is that they don't have a standard name. They are referred to with a combination of the words: electronic craft cutter ecutter cutting machine and even die cutter, which isn't accurate. What they are is very similar to a printer, but instead of ink they use a blade. The blade moves along one axis and the paper moves along another, allowing them to cut in any direction.
The first thing I thought when I saw this was, how do they cut in any direction? Do they use an omnidirectional blade? A wire? It turns out, the blade is free to rotate, which is good enough to allow it to follow the direction of travel. You have to cut most materials on a sticky cutting mat, which prevents the material from moving and cut pieces from falling out.
There are several companies that make these machines. One famous one is Cricut. The problem with Cricut's machines is they require cartridges (which presumably hold data) to work, and cannot cut designs from computer (that's what everyone said, but the new machines on their website seem to be computer controllable). Cartridges must be bought, and you have to pay for the whole cartridge with all the designs no matter how few you use. I'm guessing Cricut machines can cut better/more materials, otherwise nobody would pick them due to their cost/trouble of cartridges. Another company is Silhouette, with their famous Cameo machine. Silhouette seems to be the crafts branch of Graphtec, a Japanese company that makes commercial plotters and cutters, so they should have some experience. The Cameo is computer controlled. They have a smaller version, the Portrait, which I got and am expecting. Apparently the only difference between the 2 is the Portrait has a smaller cutting area, and their capabilities are the same. If I'm searching for their machines, silhouette cameo gives better results since silhouette portrait can refer to a real portrait of a silhouette.
I'm surprised that the 3D printing crowd hasn't caught on to this yet. The demand for 3D printers is there - it seems every month, there's a 3D printing project on the crowdfunding websites. These devices are already available, and paper can't be that much more expensive than 3D printing filament. I'm hoping to try some experiments in 3D printing. Some people have already tried it: http://www.instructables.com/id/3D-Print-with-Paper/
Speaking of Instructables, after I ordered my cutter, Instructables featured this http://www.instructables.com/id/DIY-Clear-Playing-Cards/ on making clear playing cards, which uses none other than a Silhouette cutter. What a coincidence.