When my first son was born (he will be one on the 24th of this month), I waited until a few hours before discharge before getting his HepB vaccine. Kai was fine up until then. After the vaccine, he started having retractions (not normal in any baby), rapid breathing and was gasping every now and then. Coincidence? I don't think so. I have every right and good reason to be leery of vaccines. I've seen firsthand what they can do. Doctors say moderate to severe reactions are rare, one in so many. But why would I, after seeing my newborn suffer, want to risk even that small chance? Wanna know what makes it even worse? The pediatrician threatened to sue me if I reported it. I don't have the money to go against the medical system. I felt trapped and didn't know what to do and also didn't have the time to look into it any further, just giving birth and breastfeeding (via electric pump).
Why would you risk that small chance? Because it's a smaller chance than getting the diseases the vaccines are there to prevent. Because, I hope, your child is fine despite having what you believe to have been a bad reaction to whatever vaccine he received.
You certainly don't have to vaccinate your kids (although it may prevent them from doing some things such as attending public schools) but I think the only reason so many people even consider that choice is because the diseases the vaccines have helped to prevent are no longer prevalent. If polio, for instance, was still the risk it was before a vaccine was created, I doubt most of the anti-vaccine people would have the same stance they do now.
If enough people stop giving vaccinations and some of these diseases grow in frequency, perhaps this anti-vaccine movement will lose relevancy.