1. Create a label (i.e., Saved)
  2. Apply that label to your email.
  3. Check the emails in your inbox that you want moved out.
  4. From the dropdown choose, Apply label:
  5. You’ll see the label name appear next to the email subject
  6. With the emails still checked, hit the Archive button above the emails
  7. This will move your emails out of your inbox.
  8. You can still get to those emails by simply clicking the label name on the left side menu (You may have to expand the Labels section)

I was just about to go back to Microsoft Live, but found this out from random googling.

I like a clean inbox.