In the "good old days" kids would play in the mud, run in the street and on the farm barefoot, and were exposed to a much greater degree of pathogens and developed stronger immune systems than they are today. Such is still the case in many developing countries where Westerners are almost sure to get sick, but the locals are relatively healthy, despite their "dirty" living conditions. So for this reason, Western society needs more and more vaccination to expose children to diseases that they no longer get exposed to in the environment.
The benefits of vaccination outweigh the risk, and for the small percentage that experience significant side effects from the vaccines, I believe they are the sensitive ones, and imagine what could have happened if those people had gotten the real disease, they would probably be dead. Vaccination is basically a health insurance policy.