Collectible coins, such as the 1945 Denver quarter, are often sought after by numismatists for their historical significance, rarity, and condition. The 25-cent denomination, known as the Washington quarter, was first minted in 1932 and features George Washington on the obverse. Quarters from the Denver mint can have distinct characteristics, including specific mint marks indicating their production location. The value of these coins can vary significantly based on their grade, rarity, and collector demand.