Vaccinations are a good example.
Many people are choosing not to vaccinate their children. And this is, of course, resulting with increased cases of measles, etc. Now should the parents be allowed NOT to vaccinate? What about the rights of the children not to suffer some disease because of stupid decisions by their parents? But most importantly...
herd immunity (http://en.wikipedia.org/wiki/Herd_immunity). The state has a very valid interest in seeing vaccinations happening - not because they have to care about little Johnny, but because it's better for everyone else if we don't have some people getting measles and then more people getting measles, etc...
But really just another example of our entanglement with each other and how that entanglement plays out in regards to politics, personal freedom, etc.