There's been a lot of talking lately about studies showing that exposure to ordinary grime can stave off such serious maladies as asthma. Having a dog in the house, for instance, led to lower rates of this respiratory disease in children. I heave a sigh of relief when I read these studies, as they are balm to my soul, me: the mother who didn't have a pristine house (and still doesn't) I can now pat myself on the back and say, "Hey, it was all in the name of better health!" But seriously, using antiseptic hand sanitizers constantly, and anti-bacterial soaps, have the unwanted effect of killing off the run of the mill germs that won't make us sick, but they can leave behind some heavy hitters that CAN make us very sick (C. difficile anyone?).
Even the FDA has finally seen the light and banned one of the key antibacterial ingredients in soap, because of this effect. So cut yours kids some slack and allow them to get dirty. When IS it important to wash hands (with ordinary soap and warm water?): before eating, after using the bathroom, and before touching our noses, mouths or eyes (especially if we've been around people with colds or flu).
Do take some common sense precautions to avoid nasty microbes (like E. coli in undercooked meats, or MRSA in hospital settings) but such precautions are well-served by regular soap and water. If you're going to have surgery, your surgeon will have other advice for that situation, but day to day life involves getting a little dirty. It's ok, and your kids (and their health) will thank you for it.