The first ingredient in common toothpaste, an important part of many people's dental hygiene, is silica gel. Basically, sand. It rubs away on the various things stuck to your teeth so that bacteria cannot establish a hold.
But hey, this is 2010. How about a more sophisticated solution?
A new kind of toothpaste would contain short-lived nanobots that would seek out and destroy bacteria, and collect sucrose and loose fats and proteins. That and a small amount of "wintergreen oil" to give the user's breath minty fresh.
I'm not sure how it would distinguish between a chunk of meat stuck between the user's teeth and their gums, other than not making it strong enough to lift something more than a gram. If it's too heavy, it's probably part of you.
I also specify short-lived just in case the programming malfunctions and it tries to do something strange to your mouth. If it's short lived, one can wait until they die off. Otherwise, you'd have to send more nano to stop the original nano, and the same problem recurses its way to absolute ludicrousness.