The inspiration for this post came from an answer I gave in Quora.
The most common type of case question I typically ask would involved a new product launch. I’d usually give them a few minutes to outline what they would be thinking about for a launch. This question is very helpful in gauging how much they understand our company and business. For example, at LinkedIn we have some unique ways to market and the sharpest candidates factored that into their GTM plans. It was also helpful is seeing if they have or could run a launch.
Another case question would be asking how you would figure out how to improve an existing product, or decide whether to build a new product. I'd give some parameters, a few clues about the product or market. This would be a question for a very product development product marketing role.