According to The Unites States Mint, the first U.S. coins were printed in copper and began circulating in 1793. The average life of a U.S. coin in circulation is about 25 years. After a coin has been worn down enough that it is no longer recognized in machines, it is sent back to The Unites States Mint where the metal is melted and reused. Rare dimes, nickels and quarters are generally those with earlier dates, were only minted in small numbers and are still in unworn condition.
1838 O Mint Dime
According to the Illinois Institute of Technology, the dime was first produced in the O mint (meaning it was minted in New Orleans, Louisiana) series in 1838. A rare 1838 O mint dime will have a picture of a seated Lady Liberty on one side, and a wreath on the other, with the words "ONE DIME" in capital letters. Under the words "ONE DIME" is a large letter "O," which is the mint mark for this coin.
1860 O Mint Dime
New Orleans minted only a small number of dimes in 1860, and as such these are highly prized by collectors.
1885 or 1870 S Mint Dime
The rarest dimes in the S mint (San Francisco, California) series are from the years 1885 and 1870. They are both marked by a medium-sized "S" under the wreath printed on the coin.
1874 CC Mint Dime
The rarest dime from the CC mint (Carson City, Nevada) is from 1874; the "CC" mint mark is small and appears under the wreath on the coin.
1913 Liberty Head Nickel
The Liberty Head nickel was retired in 1912, but five of them were made in 1913, making them extremely rare. One was recently assessed at $3 million.
1913 Type 2 Buffalo Nickel
Buffalo Nickels (which display an image of a buffalo) are popular with collectors. When they were first put into circulation, it was found that the year and the words "FIVE CENTS" wore off the coin quickly, so another design that fixed the wearing problem was released in the same year (type-2). A type-2 buffalo nickel in good condition is a sought-after collector's coin.
1854 S Mint Quarter
The 1854 quarter is smaller than the others minted in San Francisco around these years and can be recognized by both its smaller size and by a large "S" over the date printed on the coin.
1870 CC Mint Quarter
Minted in 1870 in Carson City, this quarter is recognized by the small letters "CC," which are broadly spaced over the A and R in the word 'quarter'. Like the 1854 S Mint Quarter, the 1870 CC Mint Quarter is smaller than the others minted around the same timeframe.