Historically, all fiat currencies have failed.
This is obviously untrue. Fiat currencies completely dominate the world
economy. They have replaced and outcompeted fiat currencies.
I'm not aware of a single country today that does not use a, currently
unfailed, fiat currency, each of which disprove the statement above.
Lars,
I suppose it depends upon your definition of failure. Let's take a look at the dollar, which as you correctly point out, is a fiat currency still in use. Whether it is a success or a failure is subject to your point of view.
The "outcompeting" of [non-]fiat currencies you refer to could be attributed to the state use of force, in the form of legal tender laws, rather than the superior characteristics of fiat money over sound money.
If you are looking for stable prices and/or a good store of value, then the dollar since 1913-1914 (when the Federal Reserve was founded) has been a dismal failure. The value of the dollar has gone down unarguably ten-to-one and more probably over twenty-to-one since then.
Further, currently we are in the midst of arguably the greatest asset bubble of all time - only partially resolved with the stock market collapse from 2000 - 2002. This bubble is being fueled by, you guessed it, the manipulation of the dollar by the Fed. Inflation is now somewhere between 3% and 6% per annum, depending upon how you measure it and whose figures you trust (and you can bet I don't trust the government hedonic-adjusted figures very much). This would put us on track for a further halving of the dollar's value in just over a decade. But we may get to experience a drastic deflation first, when the bubble bursts.
Not all fiat currencies have done as well as the dollar. Check out the history of the Argentina Peso, for example. The last time I visited Buenos Aires, I had both Old Pesos and New Pesos in my wallet; with a 1000-to-1 exchange ratio between them! Just because the Peso still exists and is in use does not mean it has been "successful".
If, on the other hand, you look at the dollar's success in funding a government run amok, numerous socialistic programs, two world wars and numerous police actions including our current 1/2 trillion dollar per year escapades in the middle east, then perhaps the dollar can be called successful. Being able to raise government revenue without having to raise taxes, quietly taking the money instead from those that have saved and using it to benefit the "government class" has been successful beyond all measure, from the politicians' point of view.
Rich