How often do serious vaccine adverse events happen?
It is often stated that vaccination rarely leads to serious adverse events.
Unfortunately, this statement is not supported by science.
A recent study done in Ontario, Canada, established that vaccination actually leads to an emergency room visit for 1 in 168 children following their 12-month vaccination appointment and for 1 in 730 children following their 18-month vaccination appointment (see appendix for a scientific study, Item #5).
When the risk of an adverse event requiring an ER visit after well-baby vaccinations is demonstrably so high, vaccination must remain a choice for parents, who may understandably be unwilling to assume this immediate risk in order to protect their children from diseases that are generally considered mild or that their children may never be exposed to.
Can discrimination against families who oppose vaccines for reasons of conscience prevent future disease outbreaks of communicable viral diseases, such as measles?
Measles research scientists have for a long time been aware of the “measles paradox.” I quote from the article by Poland & Jacobson (1994) “Failure to Reach the Goal of Measles Elimination: Apparent Paradox of Measles Infections in Immunized Persons.” Arch Intern Med 154:1815-1820:
“The apparent paradox is that as measles immunization rates rise to high levels in a population, measles becomes a disease of immunized persons.” 
Further research determined that behind the “measles paradox” is a fraction of the population called LOW VACCINE RESPONDERS. Low-responders are those who respond poorly to the first dose of the measles vaccine. These individuals then mount a weak immune response to subsequent RE-vaccination and quickly return to the pool of “susceptibles’’ within 2-5 years, despite being fully vaccinated. 
Re-vaccination cannot correct low-responsiveness: it appears to be an immuno-genetic trait.  The proportion of low-responders among children was estimated to be 4.7% in the USA. 
Studies of measles outbreaks in Quebec, Canada, and China attest that outbreaks of measles still happen, even when vaccination compliance is in the highest bracket (95-97% or even 99%, see appendix for scientific studies, Items #6&7). This is because even in high vaccine responders, vaccine-induced antibodies wane over time. Vaccine immunity does not equal life-long immunity acquired after natural exposure.
It has been documented that vaccinated persons who develop breakthrough measles are contagious. In fact, two major measles outbreaks in 2011 (in Quebec, Canada, and in New York, NY) were re-imported by previously vaccinated individuals.  
Taken together, these data make it apparent that elimination of vaccine exemptions, currently only utilized by a small percentage of families anyway, will neither solve the problem of disease resurgence nor prevent re-importation and outbreaks of previously eliminated diseases.
Is discrimination against conscientious vaccine objectors the only practical solution?
The majority of measles cases in recent US outbreaks (including the recent Disneyland outbreak) are adults and very young babies, whereas in the pre-vaccination era, measles occurred mainly between the ages 1 and 15.
Natural exposure to measles was followed by lifelong immunity from re-infection, whereas vaccine immunity wanes over time, leaving adults unprotected by their childhood shots. Measles is more dangerous for infants and for adults than for school-aged children.
Despite high chances of exposure in the pre-vaccination era, measles practically never happened in babies much younger than one year of age due to the robust maternal immunity transfer mechanism.
The vulnerability of very young babies to measles today is the direct outcome of the prolonged mass vaccination campaign of the past, during which their mothers, themselves vaccinated in their childhood, were not able to experience measles naturally at a safe school age and establish the lifelong immunity that would also be transferred to their babies and protect them from measles for the first year of life.
Luckily, a therapeutic backup exists to mimic now-eroded maternal immunity. Infants as well as other vulnerable or immunocompromised individuals, are eligible to receive immunoglobulin, a potentially life-saving measure that supplies antibodies directed against the virus to prevent or ameliorate disease upon exposure (see appendix, Item #8).