Answer by Steven Fowkes:

Yes. But it is quite rare when vaccines are not stacked, or over-prescribed.
The public health equation is the relative cost of hurting a few children (or adults) versus the public-health benefits of the majority of children and adults towards catastrophic damage (epidemic).
No informed scientist argues that vaccine injuries never happen. Public health officials and medical professionals do make that claim, or imply that claim, but the scientific studies do show that vaccines have a small chance of a negative outcome, and a very small chance of a serious, life-changing outcome. The true "insider" rationale is based on the "overwhelming" benefits of the successful vaccinations measured against the "acceptable" losses of the failures, which include both under-vaccination and over-vaccination outcomes. But this insider scientific, rational, or rationalization assessment is often lost in the politics of vaccination because many people do not want to accept any (!) loss for a public health benefit. So this aspect of vaccination policy is "spun" to be politically incorrect in "polite society."
Most people who speak or write about this are ostracized, in defense of this "containment" strategy. This especially includes medical experts and public-heath officials who are considered traitors to the cause and heretics of the faith. Some of their stories are fascinating, and will make you laugh or cry if you believe the methods employed to minimize or silence them.
In my perspective, neither the vaxers and anti-vaxers are able to legitimately claim objectivity. The not-with-my-child attitude of some anti-vaxers clearly ignores the relative values of other people to not be damaged by their child getting infected with a communicable disease. But the vaxer denials of genuine risk is, in my opinion, morally indefensible. It's a lie that violates the medical ethic of disclosure and informed consent. Since both sides are equivalently polarized for a large variety of reasons, or rationalizations if they are not on your side, the issue cannot be resolved by political means, including compulsory vaccination laws.
Regarding the latter, I tell people (here and elsewhere) how to block the adverse effects of over-vaccinations, so even compulsory vaccination policies can be effectively bypassed by any individual with a dollar and the requisite information. So, realistically, compulsion is no guarantee of actual public-health efficacy. This same thing happens when public officials pick the wrong antigen for this season's flu vaccines; it fails by any public-health assessment. It has also happened in the animal husbandry industry where animal vaccinations failed on a wholesale basis due to unanticipated food additives in the animal feed.
I hope this answer provides "the other side of the story" from that of most answers.
If you want more of the nitty gritty chemistry, read my answers to similar questions here on Quora.

Is there proof that vaccinations hurt children?