Treashunt - by technicality neither the 1937D three-legged buffalo NOR the 1922 'no D' cent are 'varieties'. They are minor die errors that gained a pile of value because of misunderstanding and tradition.
The 1922 'no D' cents are filled dies. People post them here all the time on
Statehood Quarters, nickels, cents, etc. It is a VERY common occurrence at the mint. The ONLY thing that makes these famous is the fact that there were no cents minted in Philadelphia in 1922. Back in the 1920s and 1930s when collectors first started finding and reporting these things it was believed that Philly made a short run of coins and the mintage was very low. We now know the truth...they are minor filled dies. The way I generally get people thinking is to offer them a 1923S cent with a filled mintmark for $5,000. Of course it looks like a plain-old 1923 plain worth less than a buck. But the reason my coin isn't valuable is because there WERE 1923 plain cents and they are common.
The 1937D three-legged buffalo is a simple case of die overpolishing. It was originally believed that the mint somehow 'forgot' to strike the fourth leg onto the coin, but we know now that the entire design is hubbed onto the die at the same time, and these nickels were struck with a die that had all four legs when the die was made. It was simply polished (probably to remove clash marks) and the edge of the shallow leg was polished out. Collectors have since found hundreds of different issues that have missing details due to overpolishing, but none of them gained the unwarranted fame that the 3-legger did. We have hundreds of different nickels, quarters, and cents with throats missing, bridges of noses missing, collars polished out, fronts of busts blending with the field, edges of buildings polished away - even
Buffalo nickels with the shallow feather polished away. None of them ever gained any collector interest because collectors now know that this phenomenon is common.
It was simple ignorance - misunderstanding of the minting process - that brought these coins to fame and enormously overinflated values. They suffered from the same common 'treatment' that many dies received through the years, except that these were noticed early, touted as special early, and included in all the major guides early.