Churning is the repeated application for the exact same credit card to receive additional bonuses. Based on feedback on the internet from applicants, here is a summary of which cards are churnable by bank (your mileage may vary):
American Express: success after 2 years since last application, Starwood Preferred Guest card more often if number is left off application
Bank of America: success every 90 days
Barclays: success in past with US Airways, timeframe unknown, possibly 6 months
Chase: unlikely, possibly after 3 years. Chase has a habit of bringing out new credit card products every few years. These new cards allow you to qualify for new offers.
Citibank: success after 18 months since last application, use two browser trick to apply to get two bonuses at once
See this article from The Man of a Thousand Places for a very detailed analysis.