What is the value of a US 1845 Indian head penny?

The first Indian cents were struck in 1859 so you could not have a coin with that design dated 1845. If your coin is from 1845 and is about the size of a half-dollar it's called a Liberty Head cent or simply Large Cent and is worth about $25 in average condition.

If you have a different coin please post a new question with a more complete description.