About two years ago, I started saving things electronically in my files only. It relieved some of the clutter and I even found ways to leave myself notes and tips on the documents themselves. I have recently started using Dropbox, as well.
Dropbox is awesome for pure storage. It allows you to access documents from any internet connected computer, which is a huge plus. Just like saving to the school's server, however, it is difficult to sort the items with any particular order or to mix file types.
There are tons of resources out there like Dropbox and LiveBinder that allow you to store and access files electronically. So, go ahead! This summer, clean out those closets and get rid of all that clutter! And next year, save a tree by saving your documents online instead of all that printing!