The value of an old coin depends on its age, rarity, condition, denomination and whether it is made from a precious metal such as gold or silver.
Age affects the value of coins because over time many coins are lost, damaged or made into other coins. Luckily, most coins struck since the 15th century carry dates.
Some coins were issued for only limited periods of time, which increases their value. There are also rare and collectable errors and minor variations to look out for, such as the 1955 doubled die cent.
Coin collectors use very precise terms for grading the condition of coins. In the U.S. there is a numerical system, but these designations and terms vary from country to country. Even minor blemishes can effect a coin's value.
There are always far fewer high denomination coins in circulation at any one time than there are pennies and coppers. This makes these coins more sought after by collectors, and thus more valuable.
Most high denomination coins struck before World War II were made of silver or gold of various grades of fineness. They therefore have a bullion value, or a value as scrap metal. If a coin is in unblemished condition, however, its bullion value will generally be less than its collectable value.