The value of an 1863 penny depends on its condition and variety. The most common type is the "Indian Head" cent, which was produced from 1859 to 1909. In Good condition, an 1863 Indian Head cent is worth around $1.50. However, if the cent is in Mint State condition, its value can rise significantly. For example, an 1863 Indian Head cent in Uncirculated condition can be worth upwards of $100.
There are also a few rare varieties of the 1863 penny that can be worth even more. For example, the "L/R overdate" variety, which features the date "1863" overstruck on the date "1862," can be worth upwards of $1,000.
If you have an 1863 penny, it is important to get it professionally appraised to determine its exact value.