One of the main negative side effects of vaccinations is that is can cause harmful side effects in the children who are receiving it. The CDC reports that "vaccines carry a risk of a life-threatening allergic reaction (anaphylaxis) in about one per million children." Things such as long term seizures, coma or permanent brain damage have been associated with the DTap vaccine and MMR vaccines, though these are considered very rare by the CDC. The National Vaccine Information Center also reports that vaccines may also be linked to other problems such as learning problems, asthma, and autism.
Besides medical problems that can come from vaccinations, many people believe that vaccines are wrong simply because it infringes on our rights to require vaccinations, and that the government should not be involved in a persons medical decisions. For children, they believe that choices regarding medical decisions should be made by the child's caregiver, not the government. It is also argued that vaccines are an unnatural part of the bodies immune system, and that a person's natural immune system would be stronger and would protect against more illnesses than a required vaccine.
http://vaccines.procon.org/
http://vaccines.procon.org/