Series Coins
Some coins have been issued as part of a series. The statehood quarters are a prime example. The Mint struck 50 different designs between 1999 and 2008 to represent each state in the Union. A complete collection of these consists of each of the quarters from both the Philadelphia and Denver Mints.
Commemorative Coins
The Mint has also issued coins over the years to commemorate special events and historical occurrences. These range from the 1915 coins minted to commemorate the Panama-Pacific Exposition and the 1921 Alabama Centennial to more recent examples like the 2006 coin honoring the old San Francisco Mint. Most of the commemorative coins are issued as dollar coins and are comprised of either gold or silver, making them quite valuable.
U.S. Mint Proof Sets
Collectors also prize the U.S. Mint's proof sets. These sets usually consist of one example each of five to 10 different coin denominations from a given year. These coins are struck using special dies to give them the highest quality, and are inserted into hard plastic holders to keep them safe. The U.S. Mint sells these sets directly to collectors.
Error Coins
Error coins are the namesake of the U.S. government's Mint mistakes. Plenty of coins have featured various error over the years, from incorrectly stamped dates to double-stamped coins. A guide such as "Whitman's Red Book" contains pictures of various error coins across the history of Mint coin production. Search your change as you may possess the rare 1955 double die penny which is, as of 2010, worth more than $1,000 even in poorer grades.