This isn't for everyone (i.e. those that don't live in an area with Citi branches/ATMS), but citibank has a premium banking/brokerage product called CitiGold that has all sorts of benefits. One of those benefits is no annual fees on any Citibank credit or debit cards. This means you could get the fees waived automatically on the Citi/AA Platinum Select Word MasterCard and/or the Citi/AA Premium Debit Card with no annual fees (normally $85 and $65 respectively). I believe you can also get a Diner's club card with no annual fee. There are also many high level benefits like dedicated lines at some branches, dedicated account executive, waived fees for almost every basic banking transaction you could think of, etc.

CitiGold accounts require 100K in assets with Citibank (or a 250K first mortgage), but that can be in a Citigroup Investment Services brokerage account (i.e. you just transfer some retirement mutual fund assets there to qualify).