National City, now owned by PNC, has a 4-3-2-1 Everyday Rewards Cashback card that I am fond of.
The card offer is currently geographically restricted. I got in while they were still National City and had no state of residence restrictions.
The 4% on gasoline and automotive related purchases is my cashback money maker. 2% on groceries isn't too bad either.
There are monthly spending caps on all 4 percentage categories. My spending levels never exceed them.
No annual fee (you will need to re-verify this).
YMMV on terms and availability.