Not exactly an "oddball interview question", but...
I firmly believe that I blew an interview several years ago because I was not ready to be the first to worship our new robot overlords.
Between my meeting with HR (which went well) and the guy who was to be my immediate supervisor (who seemed impressed), I had a short talk with the President's Son (whose position I don't remember, although I suspect it was something along the lines of "President's Son"). Just small talk to waste time until the next guy was ready (I thought), the conversation turned to the technological singularity. While I had read a bit about it here and there, and think of it as a distinct possibility some day, apparently this guy was ready and waiting. He asked me how soon I thought it would happen, and I kind of scoffed and said I wasn't going to hold my breath or anything. I think the correct answer was supposed to be "next Tuesday".
-- Stephen Cook