* Nail polish remover is primarily acetone. Acetone is a solvent that dissolves nail polish, but it won't significantly react with the copper in a penny.
* Pennies are coated in zinc. The outer layer of a penny is zinc, which is also not particularly reactive with acetone.
* A small amount of copper remains. While the majority of the penny is zinc, a small amount of copper is still present. Over time, the acetone might slightly tarnish the copper, but it's unlikely to be visible.
Therefore, putting a penny in nail polish remover won't cause any dramatic chemical reactions or significant changes to the penny. It's safe to say you can leave your pennies out of your nail polish remover!