The rarest modern coin known to collector's is also considered one of the most valuable: the U.S. 1849 Double Eagle gold coin. There is only one known example of this coin, housed at the Smithsonian Museum, and valued at $15 million or more.
According to 1849GoldEagle.org, this coin was made after gold was discovered in California. The large amounts of gold coming into the Philadelphia mint made it seem necessary to create a new, larger currency then the then current $10 eagle; therefore, an experimental pattern for the double eagle was crafted from a design by James Barton Longacre. It is possible there are more of these coins in existence, but it is not known for sure.