Update: These offers have changed over the years. You can find the best available offers here.
Citi is offering up to 35,000 bonus miles and no annual fee for the first year on the Citi AAdvantage Visa and American Express personal cards, as well as the business Visa. You earn 30,000 bonus miles for spending $750 in the first four months you have the card, and an additional 5,000 miles if you spend $5,000 within the first year.
Unfortunately Citi AAdvantage cards can’t be churned anymore, but if you haven’t had these cards before, this is about as good of a deal as you’ll see.
(Tip of the hat to Gary)