Sure. They can have numismatic value, their value as collectible coins. This is determined by
rarity, and condition. For example, the earliest version of the wheat penny, back in 1909, had the initials of the
designer prominently displayed on the back of the coin. This was quickly changed to a more subtle location on the front.
Coin with both the prominent intials and the San Franciso Mint mark are particularly valuable, with an average value in good condition around $900. The modified version from San Francisco is worth about $100 in good condition.