I've been taking a history class that has involved reading about the classical gold standard and the various gold exchange standards that prevailed in the western world for about a century. They all involve the idea that a country should peg the value of its currency to something else by promising to buy or sell that something else for that currency, possibly subject to additional stipulations. These days, there are many currencies that are still pegged to other currencies, but I'm not aware of any currency that is actually pegged to something else; the relative prices of various currencies are regulated, but there's nothing external to the system of international currencies to which they are tied either directly or indirectly (for an appropriate narrow conception of "indirectly tied" here).
Even the most comprehensive guarantee of convertibility always included some stipulations; at the very least, to get the US Treasury to buy or sell gold for dollars, you had to get the dollars or the gold to the right location. This meant that at most times and places there could be some deviation from the official rate. At second order, while, under the gold standard, the exchange rate between dollars and British pounds was fixed (since you could use your dollars to buy gold which you could sell for pounds, or vice versa), there were always short-term deviations that were too small or too transient to pay for the cost of shipping gold across the Atlantic ocean. While the rate couldn't move too far from "mint parity", dollars and pounds weren't perfect substitutes; they were, however, much closer than most pairs of commodities studied in economics.
This relied, of course, on the credibility of the gold standard; when countries' gold stocks started to run low, the currency tended to depreciate a bit, in fear that the country, even if it wanted to, would no longer be able to sell gold at the official price, as it would run out of gold to sell.
A few years back there was a penny shortage — businesses were having trouble making sure that they always had enough pennies to make change for customers. The classical economic solution to a shortage is an increase in price; in principle, one might have expected at least some businesses to offer 20 cents' credit for 19 pennies, for example. I'm not aware of that having happened; they seem to have limited themselves to persuasion. Even more than in the case of other goods, people have a strong sense of a "just price" for a penny, I think, and resist its being floated. In a perfect market with continuously diminishing marginal utility, the relative marginal value different people attribute to different goods should be the same, so long as each has some that they could trade; if they didn't, the relative market price of the goods would allow at least one of the two people to trade the relatively expensive object for more of the relatively cheap object to get more of what they value than they give up. It very much seems in this case as though the businesses' relative values for pennies exceeded their market prices, but, with fixed prices, they ran into quantity constraints. If the businesses could have purchased 50 pennies for 50 cents from banks, of course, they would have done so in such circumstances; however, banks, too, including federal reserve banks, were running into quantity constraints as well. The federal reserve system was, for a time, unable to defend the mint parity of the penny; I imagine that the expectation that they would ultimately be able to do so is the only reason the price stayed approximately at mint parity, and custom took over from there to keep it exact.
This idea of different denominations of physical currency representing different mediums of exchange that are held in a fixed relative exchange rate presumes that each penny (for example) is itself a perfect substitute for any other penny. There have been historical cases in which different coins of nominally the same denomination were not treated as such, and indeed it was my very recent experience with this phenomenon that prompted this post. Yesterday, in the Knoxville airport, I was given change that included a $5 bill that was stapled together; today I used that to pay for lunch. The guy who received it expressed aloud his displeasure with it; I myself wasn't particularly pleased to receive it, but didn't try to do anything about beyond pass it along in my next cash purchase. The US Treasury regards it as identical to any other $5 bill, but I imagine it will change hands rather more rapidly than the average $5 bill does, at least until it goes back to the US Treasury's shredders.