In all of my years as a numismatist--more than 50!--I have seen many prized rarities. These wonderful coins can be seen at major conventions or in museums.
The King of American coins, the 1804 dollar, may be the most famous rarity of them all. There are three distinct varieties among the 15 known examples. Three, one of each variety, are in the Smithsonian. There are two in the ANA Museum. I have seen 1804 dollars in special exhibits at shows, and once got to hold one!
Perhaps the next most famous rarity is the 1913 Liberty nickel. Five were minted. Some years ago, one was missing and unaccounted for. A well-publicized offer brought this coin out of hiding, and all five coins were reunited at a World's Fair of Money. I recall long lines to see the five nickels. I got in that line more than once.
Ten specimens of the 1933 double eagle were displayed at a World's Fair of Money. The line to see these coins reached out the main door. I also saw the two in the Smithsonian.
Perhaps the very first silver dollar struck, a beautiful 1794 holds the record for the most expensive coin. I saw this coin in a special display at a WFM.
The only 1870-S $3 is at the ANA Money Museum. I spent some time looking at this treasure.
Many more coins, famous and not-so-famous rarities...this is just a sample of the many great coins I've been lucky to see in person.