What is the value of a dollar without the phrase 'In God we Trust'?

I assume you mean a dollar bill, not a coin.

The motto In God We Trust was only added to paper currency beginning in the late 1950s, so if your bill is older than that it is not an error. My suggestion would be to post a new question giving the bill's date and series letter, if any, that appears right after the date; also please note the color of the Treasury seal.