Every year millions of trees are cut down to make paper for printing documents. This can result in the destruction of entire forests and habitats, and has prompted the World Wildlife Fund to create a file type that can’t be printed.
The WWF file type could be helpful for the environmentally conscious, especially if you’re distributing documents to some people who insist on printing everything out. Environmental reasons aside, a document that you can’t print could be a good way for teachers to distribute documents they don’t want students to bring into class or to tests like study guides.
However the document type does have its limitations--it's currently only available on the Mac (although that still means it can’t be printed on a PC, living up to its promise). In time, however, there may be workarounds for this file type, and I can’t see why you couldn’t copy and paste the document into another window.
If you’re always going out of your way to save the environment, then distributing your files as unprintable WWF’s is another way to help.