Collectible coins are categorized into various types based on denomination, historical significance, and unique features. In the United States, collectible coins include denominations such as the Half Cent, which was issued from 1793 to 1857, and other fractional coins. Counterstamped coins are those that have received an additional mark or design after their initial minting, often used for advertising or commemorative purposes, adding to their uniqueness and value among collectors. Collectors often seek these coins for their artistic qualities, historical context, and potential investment value.