Any of the diseases that we commonly vaccinate for these days--measles, mumps, rubella, chicken pox, diphtheria, whooping cough etc. All of these are on the rise because of the anti vax movement. And there are also parents who may not have properly or completely vaccinated their kids, either because of a move or change in health care providers (this was more common before portable medical records), or being forgetful, or they're too poor to have insurance (in the US) or whatever. And a small percentage of children can't be vaccinated because of health issues.
Of course, these diseases can be transmitted to adults who either never had them or are unvaccinated, but it's less common for adults (because most of us had it when we were little) to be in that situation (though becoming more common now that kids of anti vaxxers are growing up).
Oh, there's also a communicable disease that's common in young kids but not adults called "
foot, hand and mouth disease." It's rarely serious, but it can be a pain. It often sweeps through day care centers or pre schools. If you need something unpleasant but not terribly dangerous to hit toddler or pre-school aged kids without making the adults sick, this may be a good one.
There's norovirus (aka the stomach "flu"), but that affects grown ups too (people don't seem to form lasting immunity to the most common strains). Also,
rotavirus, which can be a source of diarrhea or vomiting illnesses in younger kids (less common in older kids or adults).
On the more serious end of things, there's various
meningitis diseases, which most commonly affects teens and young adults. The viral form is generally far less serious than the bacterial kinds.
