I suspect you could 'mint' some kind of paper money backed by Bitcoins using Visual Crypto.  Haven't really worked out the details.

The primary problem is the situation where someone could COPY one of the VC factors, so you couldn't easily distribute.  At the least you would need to feature a hologram/kinegram in order to prevent counterfeit.  There could be a serial number on the bill, and you could check online to see if the bill is still valid(similar to Chaum), but what is the point if it relies on an internet connection?  I would think you could make small denomination bills safely.  There is a company that does this though: http://www.bitbills.com/

-bm