In the United States we have struck coins for foreign countries since 1876. Since then, the United state has struck well over 100 years of coins for foreign nations, and in the process has minted a lot of U.S. coins overstruck on other country's coins. Some are struck on just the planchet, while others are struck on a already struck coin (creating a double-denomination.) All of these are generally scarce, and there aren't any that are "common." Double-denomination coins are always scarcer as a rule than coins which are simply struck on the wrong planchet.
The error occurs when a planchet or already struck foreign coin accidentally is struck with another nation's coinage dies. The result is a coin struck on another nation's coin planchet or a coin struck on a struck foreign coin (a double-denomination.) Some examples of these can be seen in the links below.
While this error type has occurred in the United States, it also has occurred for other nations as well, who also strike coins for nations other than their own. A good example of this is the British Royal Mint, which is the largest producer of coinage in the World. They strike numerous coins for other countries, and as a result, they make off-metals and double-denominations on other nation's coins. Here is a link to some information about the coin's they produce for foreign countries.
So, anytime you are trying to attribute an off-metal or double-denomination which does not match up with a coin from it's nation's coinage, do some research and you may find it is in fact struck on another nation's coin or coin planchet.
Here are some examples of U.S. coins struck on other nation's coins or planchets.
PCGS 1c 1982 Lincoln Cent Struck on Philippines 5 Sentimos Scalloped Planchet
PCGS 1c 1958 Wheat Cent Struck on Cuba 1 Centavo Double-Denomination MS63
NGC 1c 1919 Wheat Cent on Argentina 10c Planchet VF-20
There are numerous other examples, including U.S. coins struck on foreign gold, silver, nickel or other metals, as well as numerous examples of both off-metals and already struck foreign coins. Some collectors collect these by finding a favorite country or continent and collecting U.S. coins struck on foreign coins from those countries or continents, while others will simply try to get "one of each" of every known basic type (U.S. cent on philippine 10c; U.S. cent on Argentina 10c, etc.)
Coins struck on other foreign coin planchets and struck coins provide and endless array of interesting and varying Mint mistakes, which leaves the opportunity to find or discover something new (such as a new U.S. on foreign) as a possibility.