I've had the "write code that does..." questions in interviews, and I've enjoyed them.
Personally I've been through one interview with "write code that does..." and I really disliked it. But in part that was due to the fact that I was given a pen and paper (yep, pen, no erasing here). I don't write code on paper.
I was able to get a snippet of code that would work, but I write slowly -- especially if I'm trying to write legibly. So the whole thing made me uneasy and very self-conscious for the rest of the interview. If I'd been given a computer to type up the code (even a computer with nothing but Notepad) it would have alleviated a lot of anxiety. But maybe that's just me.