The writer of a blog called TeachPaperless is promoting a campaign to get teachers to sign up to not use paper on Earth Day. I haven't committed. But the fact is, I'm using much less paper than I did only a couple of years ago. Things I used to hand out I now put on Moodle as PDF's. With the Moodle version of Reader, students can't write on the page (we have tablets), but they can easily transfer to Word or OneNote and do so (as a freshman taught me). I also have the option of projecting things to a screen.
There are a couple of things that I have had students hand in on paper still, but most work goes through Moodle, or now, on a blog.
Tests are still on paper (though I've done some Moodle quizzes). But I am fairly close to... paperless. Well, time to go back to grading some online essays.