Is there any way to tell which ones?
Some things are listed as potential triggers: an allergy to eggs or latex can indicate potential life-threatening problems with vaccines.
Our oldest started life vaccinated--and within the first eight months of her life, had 5 bladder infections, 7 ear infections, and seizures after every single injection.
We stopped, on the advice of a neurologist. The only lasting damage has been an enamel defect on the permanent teeth that were beginning to form during that time (the sudden high fevers that caused the seizures were not good for enamel formation); a good dentist has been able to correct all of it on her front teeth, and even with the damage, she's had no problems with tooth decay.
Since stopping, she's not had a single seizure. She's had two colds. No ear infections. One bout of flu. No bladder infections. No persistent coughs. She's played with chicken-poxy kids and shown no clinical symptoms. She's nearly eleven now.
Going back to my mom, dad, and siblings (the only members in our family to have been vaccinated), my dad and multiple siblings had severe reactions to vaccines. I got to delay starting college by two weeks when I came down with a lovely case of measles from the mandatory measles booster.
Vaccines can't be tolerated by everyone--so for those of us who cannot reliably vaccinate, there are things we do to minimize all risks. Things like never having our kids in day care (not even church nursery); teaching excellent hygeine practices; doing selective, individual, and delayed vaccination (such as tetanus by itself, without diptheria or pertussis), etc. We've had the help of some great medical practitioners who are supportive of our options, and were able to give good advice for minimizing risks (the big one being: don't do any international travel until the kids are in their teens, and have been selectively covered)
Not everyone who opts out of vaccination is doing to out of some amorphous "fear"--some of us have very solid medical reasons.
Most parents don't even bother reading the inserts. There are a number of reasons certain children shouldn't be vaccinated. Illness, previous severe reactions, and so on.