In Japan no response can be the most polite response at all. And not in the "if you can't think of anything nice to say don't say anything at all" type of way either. If you don't want to refuse something or turn down an offer or deal with a problem, you simply don't respond. It is the most polite way out, as face is saved all around. The asker isn't ashamed by having to be refused/turned down/the cause of unpleasantness and the askee isn't ashamed by having to refuse/turn down/cause unpleasantness. Its a win-win situation!
Except if you're an uncultured barbaric foreigner like myself, without an appreciation for the finer niceties of social interaction, and an over-developed worry gene to boot. Then you'll find yourself less worried about face and more worried about heards of elephants or flash floods having taken out the recepient of your email/letter/telegraph/carrier pigeon.
Afterall, parents do also tell their kids to "use their words," right?