I have had some luck with, "I wish I could give you the answer you want, but I can't." Or, I may say something along the lines of, "I understand you are frustrated, but I simply do not have the authority to grant your request."
There are definitely times when no answer is better than any answer you can come up with, though. I work for a small, family-owned store. People come to us because we have very specific items that you may be able to find in a big box store, but you won't find the selection and the accessories. Our first priority is, of course, to ensure that they come back to us. But when an extremely difficult customer throws out a threat of taking his business to the big box store, I find that a patient smile and no verbal response is better than anything I can say. Plus, it keeps me from saying, "Let me get the door for you!"