1804 Dollar: The King of U.S. Coins The 1804 dollar is among the most coveted of all U.S. rare coins, with only 15 known examples. Strangely enough, no dollars dated 1804 were actually struck in that year. The United States Mint only struck dollars dated 1803 in 1804; there was a silver shortage and the expense of creating a new die was saved (regular.