Some rare U.S. coins a person might find in his coin jar include the 1995 double die penny, the 1943 steel penny and the "In God We Rust" 2005 Kansas state quarter. Other rare coins include the Ben Franklin half dollar and 1942 to 1945 silver nickels.
A double die coin occurs due to a misalignment in the minting process that causes a double printing of the letters or numbers. A small number of 1995 pennies feature this double die error, which caused the words "Liberty" and "In God We Trust" to look slightly blurred. As of 2015, the 1995 double die penny is worth approximately $20 to $50. There are also a small number of 1955, 1969 and 1972 double die pennies; uncirculated 1955 double die pennies are worth more than $25,000.
In 1943, the United States decided to make pennies from steel in order to save copper for the war effort. An error led to the production of a small number of copper pennies that year, approximately 40 of which are thought to still be in existence and can be worth as much as $100,000. The 1943 steel pennies are also a collector's item, worth between $0.50 and $10.