What is the rarest or most valuable coin in the world to collectors?
To define the rarest, most valuable coin would be difficult. There are a number of coins that would be candidates, including the 1933 double eagle mentioned. The Brasher Doubloon, the 1913 Liberty nickel, the 1870-S Three dollar gold piece, the 1804 Silver Dollar, and others would be in the running. The value of such a coin depends on a number of factors, not the least of which is how well the owner is promoting it. The country of origin is another factor, as well as the coin’s pedigree (who owned it in the past… anyone famous?) Depending on the collector, “value” may be a broader concept than mere monetary value. More on that here: http://www.valuable-coin-stories.