I used to use auto payment for my cellular phone bill until they took out a double payment one month, and then didn't give me credit for a cash payment the next (thus charging my card for the full amount when it should have only been charged for half).
It's a lot harder to get your money back after they've already taken it because companies then just count it as a credit instead of giving you a refund. At the same time auto payments can be a good tool for avoiding late fees.