What is the value of a 1968 liberty penny?

One cent. Huge numbers were minted and they still turn up in change.

To clarify things, it's called a Lincoln cent. "Liberty pennies" carried a picture of Miss Liberty and were minted from 1793 to 1857. Coins with the Word LIBERTY on them as opposed to a picture of Miss Liberty are always referred to by the name of the design or in some cases the coin's artist; e.g. Morgan dollars.