Could you please describe typical stages of software product or service lifecycle?
Look for a clear understanding of typical software lifecycle processes: requirements, design, implementation, testing, implementation, support. A discussion may ensue on what each of processes might involve.
How waterfall is different from agile? Which would you prefer?
Look for clear understanding of underlying principles, strengths and weaknesses of both approaches. A good candidate will have a balanced view and will be able to evaluate development process on the merits of a task at hand.
Mention then to any Agile/XP/Scrum adepts that NASA uses waterfall to develop software in control of space rocket systems, and then ask if they could give their opinion as to why what NASA does is different from the job they are applying for?
Waterfall evangelists should be able to explain why iterative software processes seem to have gained so much momentum in recent years without attributing the popularity entirely to hype or fashion.
Based on the discussion under which circumstances would they use waterfall and when agile?
Looking for a meaningful answer that brings include some actual decision criteria such as: existing processes, level of user involvement, level of testing and build automation, developers proficiency, safety and legal requirements, nature of software etc.