Stacks Bowers Galleries is auctioning what they describe as "Quite Possibly the Very First Silver Dollar Struck" at 6pm EST in New York, the "Amon Carter" 1795 U.S. silver dollar. This coin still retains some reflectivity on its 219 year-old surface, and has been graded "Specimen 66" by PCGS. If this coin were not unique for its spectacular condition, it would be for the fact that it is the only coin known to use the particular obverse and reverse dies used to mint it.
Another interesting characteristic of this coin is that was both filed and plugged before being struck. Early coin planchets were not made to a very close standard when the Mint began, so each individual blank had to be weighed. If it were too heavy, it would be progressively filed down until it was the correct weight. If the blank weighed too little, an 8mm silver plug was inserted into the center before striking.
In this coin's case, it was apparently overweight originally, but someone filed off too much and it had to be plugged to bring it back to the correct weight. You can see the plug on Liberty's cheek in the image above.
Greg Reynolds, who has actually held this coin in his hand, has a detailed and captivating article on this coin at CoinWeek.
Oh, and before you start counting your spare change, bidding is starting at $2.2 million.