Vaccines can eradicate disease and prevent serious illness and death. Mandatory vaccination has eradicated diseases that once killed thousands of children, such as polio and smallpox. According to researchers at the Pediatric Academic Society, childhood vaccinations in the US prevent about 10.5 million cases of infectious illness and 33,000 deaths per year. 
According to the American Academy of Pediatrics, most childhood vaccines are 90-99% effective in preventing disease. When children who have been vaccinated do contract a disease, despite being vaccinated against it, they usually have milder symptoms with less serious complications than an un-vaccinated child that gets the same disease. 
The risks of not being vaccinated far outweigh the small risks associated with vaccination. Preventable diseases like measles and mumps can cause permanent disability and death. In 1991 an outbreak of measles in an un-vaccinated group of children in Philadelphia caused seven deaths. Children infected with the mumps can become permanently deaf. 
The claim that vaccines cause autism is false. Many studies, including one by researchers at the Centers for Disease Control and Johns Hopkins University School of Public Health, reject the hypothesis that thimerosal, a mercury-based preservative in vaccines, causes autism. 
Even when diseases seem to no longer exist, outbreaks can still occur if children are not vaccinated. In Boulder, CO, fear over possible side effects of the whooping cough (pertussis) vaccine  led many parents to refuse vaccination for their children causing Boulder to have the lowest school-wide vaccination rate in Colorado for whooping cough and one of the highest rates of whooping cough in the US as of 2002. 
No, children should not be vaccinated because...
Governments should not have the right to intervene in the health decisions parents make for their children. 31% of parents believe they should have the right to refuse mandated school entry vaccinations for their children, according to a 2010 survey by the University of Michigan. 
Vaccines are often unnecessary in many cases where the threat of death from disease is small. During the early nineteenth century, mortality for the childhood diseases whooping cough, measles, and scarlet fever fell drastically before immunization became available. This decreased mortality has been attributed to improved personal hygiene, water purification, effective sewage disposal, and better food hygiene and nutrition. 
Common childhood vaccinations may cause rare yet serious reactions including anaphylactic shock, paralysis, and sudden death. This risk is not worth taking, especially considering most diseases vaccinated against are not necessarily life threatening. 
Vaccines can trigger auto-immune disorders such as arthritis, multiple sclerosis, lupus, Guillain-Barré Syndrome (GBS), and other disorders. 
Vaccines clog and disrupt the lymphatic system with large foreign protein molecules (the active ingredients contained within vaccines) which may lead to lymphatic cancers such as leukemia and lymphoma. 
All vaccines cause immune system suppression, and can permanently damage the natural immune system. Unvaccinated children build and strengthen their immune systems through fighting off infection and developing natural immunity to diseases like measles and chickenpox. Artificial immunity, generated through vaccination, weakens the immune system and leaves children more vulnerable to all other diseases and infections.