Banks like Chase and Citi often have special promotions where they will give you 10,000, 20,000 or more free frequent flyer miles on American Airlines, Delta or United if you will just open a checking account using a special code.
Normally you have to do some special activities (like set up direct deposit, or make 5 debit-card purchases) and keep the account open for several months, but at the end of that time you should be rewarded with the promised miles.
One particular online bank, BankDirect, gives American Airlines AAdvantage miles just for keeping money in a checking account. The account has a monthly fee of $12. Every month they send the miles to AA, just like clockwork. At the time of this writing the value of the miles beats the interest that you would get in a normal bank account, so it’s worth doing if you have some spare cash.