Even if you can't get paperless, these strategies will help reduce the amount of paper you have on your desk, in files, etc. I like the "scan & shred" as a way to reduce paper kept. You could scan and store in folder in files backed up to a server, Google Docs, or Dropbox. For more sensitive documents, I would store in files that are stored on a school server that can be passed along, when necessary.
Here are some good tips on how to streamline the information you face on the Internet, email, etc. Like Jodie, I'm working to implement the GTD organizational system using Evernote & Web Clipper, Diigo, Google Mail, Google Reader, Twitter, Google Drive, etc.