Origami is covered by the same copyright legislation as other artworks. The availability of images and instructions mean that a creators’ work can be replicated. However, the rights of the final work still remain with the designer and should be respected.
I am a member of a group of origami artists that monitor origami usage and follow up on any infringement of copyright rules. Origami Authors and Creators OAC - http://digitalorigami.com/oac/