Rarity
Coin collectors are willing to pay more for a coin if there are fewer of those coins available. Two factors can make a coin rare. Some are minted in very small quantities. Others were minted in larger quantities, but few survive in desirable condition. It is simple to find out if a particular coin is rare. Go to a website listing coin values, like the one provided in the Resources section. Search for the denomination, year and mint mark. If the prices are high then the coin is rare.
Condition
Condition is an important factor in a coin's value. Some common date coins are very rare in uncirculated condition and therefore quite expensive. Some date and mint mark combinations on certain coins are so rare that they are valuable even in poor condition. In general the better the condition of a coin, the rarer it is and the more it is worth.
Demand
Some coins are rare because they are so popular. Coin collectors covet famous coin rarities like the three-legged buffalo nickel, 1916-D mercury head dime and 1909-S VDB Lincoln penny. The competition to own coins like these is so intense that their price is higher than other coins with similar mintage figures.
Extreme Rarities
Some coins are so rare that they are practically unique. Examples of these are the 1943 copper cent, 1913 liberty head nickel, 1974 aluminum cent, 1908 draped bust dollar and 1933 Saint-Gaudens double eagle gold $20 coin. Only a handful of these coins were made, so they are worth millions of dollars each. A 1933 Saint-Gaudens double eagle gold $20 coin sold for more than $7.5 million.
Errors
Error coins are truly unique. No two are exactly the same. If a coin contains a flaw because of a mistake in manufacturing, it has value to some collectors. Errors include clipped planchets, multiple pressings and overpolished dies that erase design details. The more blatant the error, the rarer the coin and the more it is worth.