When I was due to pay my annual fee, I called Citi and asked to speak to a "customer retention specialist". He agreed to waive the annual fee if I charged $1,000 to the card in 3 months.
Even if you don't fly AA a lot, I think an AA card is worthwhile because you're able to board in the first group of non-elite passengers, so you won't have to gate check bags. If you don't have an AA card and aren't AA elite, you'll probably have to gate check bags, because bin space will be gone by the time you board.