I once encountered a job application that asked me to list my magazine subscriptions.
You can imagine how much I had to resist putting down some truly bizarre publications. It didn't matter. Despite my safe answers, I didn't get the job.
I can understand what the employer may have been trying to achieve. They wanted, I guess, some indirect look into my real personality; a glance at what is hidden behind the carefully-worded interview answers.
Which brings me to this question: Setting aside any worries about violating employment laws, if you could pick an unconventional question that would stand a reasonable chance of revealing important information about an applicant, what would that be?