There is no question that vaccines are vital to individual and public health and should be required as a matter of law. Nor is there any question that they do not cause autism. This notion has been shown to be completely unfounded and was discredited by the scientific community. However, in the interests of complete accuracy, it should be noted that vaccines are extremely dangerous to those who have a compromised immune system, for example, someone on chemotherapy or someone with AIDS. And when people refuse to get their children vaccinated, not only are they putting their own children at risk, but they are also putting at risk those with weak or non-existent immune systems. These are the people who must rely on everyone else being vaccinated because they simply cannot be. We call this "herd immunity." Without a critical mass of vaccination in a community, the "herd," we are putting at grave risk the weakest amongst us. It is this danger of vaccination, completely avoidable, that makes the position of the anti-vaxers so appalling. The immune-suppressed are people who must depend upon the kindness of strangers. For them, it is a matter of life and death.
The simple answer is that vaccines are responsible for much of the decline of infectious diseases in the past few centuries. Far from being dangerous, most vaccines can prevent you from catching many deadly or disabling diseases, with a very small risk of bad side effects. The most common side effects of vaccination are simply a small amount of local soreness. Although a few people who are allergic to eggs may have issues with some vaccines, medical personnel administering vaccines take a medical history to make sure vaccines don't harm people.
There is no evidence of vaccines causing things like autism, despite the fears of a few ill-informed celebrities. Not giving a child the proper vaccines is almost a form of child abuse because it means not protecting children from dangerous diseases.