I'm opposed to many sorts of state interventions, but public health measures strike me as a no-brainer. I mean real public health measures: not nannying people about their trans-fat consumption, but preventing the transmission of infectious disease. The negative externalities of infection seem to me to give the state a perfect right--indeed, an obligation--to curtail your freedom to fanny about spreading cholera.
As Matt Zeitlen says, I do not recognize the "right" of parents to refuse to vaccinate their children.
It goes without saying that I don’t share Jesse Odegard’s sentiment that Marlyland needs to “stop being so dramatic” in mandating that kids receive basic shots or else not be allowed to attend school along with fining the parents for each day absent. Of all civil liberties, I don’t see the one to pigheadedly endanger and inconvenience children, who by law have to attend public school, with your un-immunized, disease-ridden child because you’re too twee to see your kid get some shots as one that needs urgent protection.
Vaccines work primarily not by protecting you, but by creating "herd immunity": denying the virus a reservoir in which to incubate. Public schools* used to be the perfect incubators, because there you have large numbers of people with no prior immunity herded together, making disease transmission a near-certainty. Vaccines have destroyed those disease reservoirs.
Now that the disease reservoirs are destroyed, of course, parents are tempted to free ride on society. They trust in other parents to vaccinate their children, thus maintaining a disease-free environment in which their own precious princes and princesses can run around safely without taking precautions. They do this for reasons logical and illogical--vaccines do pose some very small risk to kids, but more of their fears seem to be based on junk science like the thimerosol-autism connection. But even their real fears about the safety of the vaccine would be vastly outweighed by their fears of disease if other parents didn't vaccinate, so it's accurate to describe their behavior as free riding.
This behavior shouldn't be allowed for two reasons. First of all, contrary to popular belief, vaccinations don't necessarily provide lifetime immunity; that's why the vaccine's role in destroying the disease reservoir is so critical. If enough kids aren't vaccinated, they'll create new reservoirs, as has already happened in some places with diseases like measles and whooping cough. Adults whose immunity has attenuated over time catch the diseases, and as we all know, diseases you get as an adult are much worse than the same diseases are in kids. Refusing to vaccinate your kids thus endangers other peoples' lives.
Second of all, there's no way to create a social policy that says "90% of all children have to be vaccinated". Are we going to hold a lottery for the remaining 10%? Unvaccinated children are a direct menace to public health, which makes it reasonable to forbid them from going out in public.
* By which I mean, before you start screaming, "schools attended by members of the public", not the government-run school system.