Collectible coins can include a variety of denominations and issues, such as the Half Cent, which was produced in the United States from 1793 to 1857. The 1871 coinage from the Philadelphia Mint is notable for its historical context. Hawaii had unique coinage during its period of monarchy before becoming a U.S. territory, which is sought after by collectors. Coins can be valued based on rarity, condition, and historical significance, impacting their desirability in the marketplace.