Are there any valuable 3 cent stamps?

Sure! There are some very early 3 cent stamps that in mint, or unused, condition and their original gum that are worth $70 to $90. These would have been issued around the 1900's. Even used a few of these would sell for a few dollars. Since then, unless there is something really unusual about them, they aren't going to be more the a few cents. But there are always some errors and rarities! Check out a catalog at your local library.