The "weird" questions are the converse of the "fizzbuzz" questions: You need to have a specific reason for them, not ask them "just because" or you're looking to "stump the chump".

I interviewed for a job one time where they asked: "If I asked you to make me a peanut-butter and jelly sandwich, what would you do?" In the context of the position I was interviewing for, it made perfect sense. We were dealing with people with disabilities and they were looking for people who would try to draw out someone further and even empower others by responding something like, "Tell you what, I'm hungry too. Let's both go make one. Have you ever made one before? Want to learn?" They would also follow up by dialoging with candidates about whatever they did answer.

In interviews for other types of jobs, I'd be looking for the guys with the white coats and butterfly nets were I asked the same question. Hiring is a difficult, risky process and any such question - if asked at all - should be something that's purposeful and part of a larger process.