I think Cletus gave a good answer to why these questions are used in interviews in this post: http://news.ycombinator.com/item?id=5264510

In short, if you can't write a simple FizzBuzz program, then you are probably not a good developer. Questions like these are good for being a quick way to separate programmers from those who cannot program at all.

But I agree - as someone who sucks at puzzles under pressure, questions like 'what's next after 111221?' seems like a totally retarded question to me.