Is any national currency redeemable in gold?
No, none of them.
Is any currency backed by gold? (i.e. does the central bank hold a large amount of gold in relation to the money that they issue)
The CHF used to be backed by 40% gold by law. This is no longer the case. When Switzerland joined the IMF in 1999 this became illegal by IMF rules.
Switzerland is now selling a large part of its gold reserves (as are other European central banks). While increasing its money supply greatly (how else do interest rates go to 0.75%? drastically increase the money supply to push down interest rates)
CHF maintains it correlation with gold due to its history but not its present practice.
Ferdinand Lips would be the person to look to regarding information on the CHF and gold.
http://www.financialsense.com/Experts/2003/Lips.htm
http://www.fame.org/goldwars.htm
AUD has a very low backing of gold. The Reserve Bank of Australia sold of most of its gold reserves in the late 90's (about the same time that Gordon Brown sold off the UK's accumulated wealth of 1500 years for 250 USD/oz). Australia in fact ranks behind small non gold producing countries such as Lebanon and Tunisia in terms of gold reserves.
Canada even more so:
"Canada has sold its entire holding of 1023 tonnes, making it the only G7 nation that has no gold backing for its currency."
From
http://www.safehaven.com/article-1365.htm
AUD and CAD may be correlated with gold but this is because the private sector in these countries produces and exports a lot of gold (as well as other commodities).
The US is the largest holder of gold reserves. How much of this is still in Fort Knox PHYSICALLY and not just on paper is another question as much gold is loaned out for the whopping sum of 0.20%! In essence the US has sold a lot of its gold into the market through gold leasing (even though it still shows up on the central banks books as a asset (accounts receivable)). Whether they can call in these loans and get the bullion back?
Germany and other EU banks are large holders but they are selling their gold reserves too.
Which countries are increasing backed by gold?
RUB the Russian central bank is increasingly adding to its gold reserves in lieu of USD's. And Argentina if you would believe it who told the IMF to basically go jump and bought gold reserves to add strength to its currency (and it worked).
Also the INR (Indian rupee) would be de-facto backed by gold not by the Indian central bank holding reserves but because private Indians are the largest consumers and savers of gold.
Basically have countries that produce and export a lot of gold Australia, Canada, South Africa, Russia, Brazil may be examples here.
Or countries who’s central banks still hold large gold reserves (if decreasing CHF, EUR, USD).
Or countries that are increasing there gold holding (e.g. Russia, Argentina via central bank India via its private citizens).
But there is no real substitute for the real thing!