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Each company and each card has its own churning possibilities, rules and wrinkles. The stock answer is that Chase cards generally can't be churned (they will give you the card but not the bonus), Citi cards often can be churned, and AMEX has a section in the terms and conditions of each card detailing exactly how to churn that particular card (unfortunately without circles and arrows).

Start here http://www.flyertalk.com/forum/credi...-programs-599/ for most cards, and here http://www.flyertalk.com/forum/chase...ewards/1487603 for UR earning cards. You will find most of your specific questions answered, feel free to ask any others.