Originals in the safe, with other important documents. Copies hung on the wall in my office. I worked and paid a ton of money for them, and I'm proud of them. I've needed to provide proof of diploma for certifications/licensing/etc, so no way will I ever shred them. Plus, if your school burns down or loses all their records somehow, you'll be screwed if you ever have to provide verification of your degree. I know that sounds remote, but it's happened to a couple of friends now, and had they not had their own records, they wouldn't have had proof of completing their MA.
BTW, you don't need to frame them all. Just choose one (maybe the biggest, or get a big matting), and stick them all in the frame with only 1 showing. Voila! Pride and containment.