I don't have kids myself, but I hear that they can be kind of messy at mealtimes. The solution: a platform that is clamped to the table with suction cups holding the bowl or plate in place.
Unfortunately, you can't actually clamp the food onto the plate, so my guess is that kids will simply change tactics on you by scooping up the food with their hands and hurling across the room. Face it, you just can't have nice, clean things anymore. [Wireless Catalog via 7Gadgets]