What you see above is a short part of a student's marked, revised essay (from four and a half years ago). That I could easily find the essay to use for my screenshot already gives you my first reason for grading online. With organized folders (that are simple to create), I can keep students' work and access it easily for writing letters of recommendation, finding examples for current students, and illustrating my blog (though I admit I'm unlikely to need more blog examples after today). I would not be able to do the above with essays submitted on paper or Word.
More important than the benefits to me, I like that my students, without additional effort, keep a record of everything they've composed for my class. To improve, students should be looking back over the work they complete and the feedback they receive. They should track the success of various approaches they've tried. The better their record keeping, the more likely they are to be able to remember to avoid what didn't work and to employ what did.
For those of you in my age bracket and older, you might remember nights like my worst in college. At 6:00am after an Oreo-fueled all nighter, I completed the ten-page paper due that day. When I went to print (on my dot matrix printer), the computer crashed and I hadn't saved in hours. While I remembered enough of my essay to recreate the ideas, time spent in revision and editing (or asleep) would have done more for my education than the hours I spent recreating what I had already done. I love that Google Docs save automatically.
And on documents that my students and I share, they can see my comments/suggestions as soon as I make them. This way, they get their essays back faster than they would if they had to wait until our subsequent class. Further, once I know that some students have markings they can see, I'm spurred to complete the rest of the class's grading so that all students get their essays back together-ish.
I admit that the good people at Google haven't perfected some formatting issues, but I trust that they're on the case. What aspects of reading, writing, and grading do you prefer online over on paper? If you've ever been a student, what forms of essay submission do you prefer? Please share your thoughts in the comments.