One of the most expensive, popular, and desired types of errors are the double denominations. This error happens when a coin is struck on a previously struck coin of another denomination.  Examples are a cent on a struck dime, and a nickel on a struck cent. The most dramatic are those with considerable design visible from the original strike. There are a few known  double denominations with different dates. The error illustrated here is a 1999 Cent on a struck Dime from 1997- 2 years apart!

Images courtesy of Byers Numismatic Corp.

Significant examples:
1999 Cent on a 1997 Dime, PCGS MS-66 (illustrated above).

2000-P Sacagawea Dollar struck on a Massachusetts 50 States Quarter Dollar

2000-P Sacagawea Dollar struck on a Maryland 50 States Quarter Dollar

Sources and/or recommended reading:
"Double-denomination coin appears in change", COIN WORLD, September 24, 2001, pages 3 and 110