Circulated 1963 pennies are only worth face value, however a penny in mint, uncirculated condition can be worth anywhere from $.05 to $.35 or more, as of 2014. The value of the penny is greatly dependent on the condition the penny is in.
Since there is no actual grading scale for the value of a 1963 penny, it can be difficult to determine the true value of the coin. If a penny is in extremely worn condition, it can often be concluded that it will be graded as poor. Pennies that look like they have come right from the mint will be graded as excellent condition and will be worth more than a penny of a different variety would. In between the poor and the excellent conditions, the grade of the coin is greatly dependent on the seller as well as the buyer.