Special coins can be defined as coins that are different and unique; something that is not manufactured anymore. Coins last longer than paper money and so there are still many special coins that are being circulated every day. Rare coins can be worth a lot of money. If you are able to find coins that have not been used (circulated) a lot and are not made anymore, collectors may be willing to pay top dollar for them.
Look for coins dated prior to 1964. After 1964, the materials used to make coins changed. Dimes and quarters made prior to 1964 are made of silver. Pennies made prior to 1964 are made of solid copper.
Look for half-dollar and dollar coins. Half dollars made prior to 1964 are made of silver.
Look closely at the Minting location. This should be listed as one letter in the front of the coin. Coins made in certain places in certain years may be worth more than coins made in a different location. For many 1964 "D" nickels made in Denver Colorado have a spelling error in their "E Plurbus Unum".
Look behind pennies. "Wheat Ear" pennies have two wheat leaves around the word "One Cent" on the back. These pennies aren't worth too much more than an average penny, but are good for a starter coin collection.
Look for steel pennies. These used to be easier to find, but now collectors have snapped them up. Steel pennies were minted in 1943 when the US was attempting to stock copper for the war effort.
Look for imperfect coins. The US mint has very extensive quality control measures. Coins that have been struck improperly are worth considerable amounts of money. The 1970 "Atheist cent" penny was stuck with a broken die. The penny simply states, "In God".
Look into gold coins; specifically gold coins made around 1849. Many US gold coins made around this time were made of gold mined during the Gold Rush. Because the Gold Rush is a historical time in American history, they can be very valuable. Most of these are hard to come by. A rare £13 gold piece from 1854 recently was given a 2.5 million-dollar price tag.
Look at "die rotation". Is the imprint behind the coin level with the imprint on the front? If not, this coin could be valuable.
Never attempt to polish rare coins.