Origami

ORIPA is the closest thing we have to CAD for origami. It's based on Java, although it does have binary builds for several major platforms. I couldn't get the Windows build to work, so I installed the OpenJDK and used the .jar file. The program is essentially based on editing a crease pattern, allowing you to visualize the final model in 3D. One of the killer features is that you can export the 3D view as a mesh, which means you could potentially edit it for 3D printing or create nice renders of your origami designs in Blender. It has many fold options available and should accommodate various origami styles.

I think one of the more promising ways to use this is to use it in tandem with a physical prototype for designing origami, as this gives you a clean template when you arrive at a design that you like. Some people have also mentioned that they design origami in this program before they ever fold it, which seems fairly difficult to me. Still, it's the closest thing I've found to a CAD program for origami, and it has a lot of features that make it genuinely useful. It's a bit rough around the edges, but it is a true little open-source gem that I imagine is easily overlooked for people new to origami.