As others have noted, basically every bank in the US offers credit cards, but I do make use of American Express as my primary purchasing method, and for me this is a feature and not a bug.

They offer excellent customer service, the concierge offering has done quite a few excellent things for me (for free!), every time I have had to perform a chargeback the experience has been painless and the investigation concluded quickly, they generally have promotions related to merchants I frequent, etc. It's a much better experience as a customer than any bank I have ever had an account with.