One of the things that motivated me to learn Moodle was the possibility of a paperless classroom... well, that and the fact that there always seems to be someone using the photocopy machine. So yeah, a paperless classroom.
One of the features I love about Moodle is the fact that students can upload digital assignments to the course in which they are enrolled. This means I have access to papers and handouts by way of my Moodle installation and my students never have to turn in hard copy assignments. Ok, I realize what I just described sounds an awful lot like email, but here's the catch.
I can grade the assignments in the Moodle installation, itself. I can literally leave feedback and post the grade to the grade book on the same screen. This is great news for two reasons. One, I provide the most immediate feedback to my students possible. They don't have to wait until the next day. They don't have to wonder if I lost their paper. They simply need to log in to the course and check the grade book for their grades. Once I post it, it is available to the student. Second, I don't have to tote around folders of assignments, keep the organized, and then transfer grades to the grade book. It is all done right then and there within the Moodle framework.
It's like we have removed three (proverbial) middlemen... or at least three literal steps in the grading process.
The following video explains how a student uploads a file in Moodle.