I suspect that there could be privately issued, pure paper currencies which, in free competition, will tend to be reliable. However, I cannot imagine how they wouldn’t be based on a commodity standard of some kind, and I think that the commodity will be a precious metal.
There are several companies that do this with varying degrees of libertararian leanings. E-gold was founded by some gold bugs/libertarians. They had the gold stored in vaults in the US and they had accounting firms audit the gold in storage. The problem they had was the government didn’t like them much and they were used by a lot criminals so under that pretext the feds after long running arguements with the company eventually raided the place and effectively shut them down and seized all the gold. There is already an existing market in the trade and exchange of online currencies backed by gold and silver.
I see the ideal gold backed currency to have the gold stored privately and secretly with independent audits but with the exact location of the gold a closely guarded secret with multiple secure locations. On the site I am developing right now I plan to have the gold displayed 24 hours a day with a live web camera so you can always see your gold in storage to inspire additional confidence.
One thing I haven’t seen mentioned here is the practice of MONOPOLY of money by governments. This is prehaps the best way known to and practiced by mankind for putting a strangle hold on other people’s activities and ownership don’t you think?
Jain