From The History of Vaccines website (a new project of the College of Physicians of Philadelphia):
Health and medicine scholars have described vaccination as one of the top ten achievements of public health in the 20th century. Yet, opposition to vaccination has existed as long as vaccination itself. Critics of vaccination have taken a variety of positions, including opposition to the smallpox vaccine in England and the United States in the mid to late 1800s, and the resulting anti-vaccination leagues; as well as more recent vaccination controversies such as those surrounding the safety and efficacy of the diphtheria, tetanus, and pertussis (DTP) immunization, the measles, mumps, and rubella (MMR) vaccine, and the use of a mercury-containing preservative called thimerosal.
Widespread smallpox vaccination began in the early 1800s, following Edward Jenner’s cowpox experiments, in which he showed that he could protect a child from smallpox if he infected him or her with lymph from a cowpox blister. Jenner’s ideas were novel for his time, however, and they were met with immediate public criticism. The rationale for this criticism varied, and included sanitary, religious, scientific, and political objections.
For some parents, the smallpox vaccination itself induced fear and protest. It included scoring the flesh on a child’s arm, and inserting lymph from the blister of a person who had been vaccinated about a week earlier. Some objectors, including the local clergy, believed that the vaccine was “unchristian” because it came from an animal. For other anti-vaccinators, their discontent with the smallpox vaccine reflected their general distrust in medicine and in Jenner’s ideas about disease spread. Suspicious of the vaccine’s efficacy, some skeptics alleged that smallpox resulted from decaying matter in the atmosphere. Lastly, many people objected to vaccination because they believed it violated their personal liberty, a tension that worsened as the government developed mandatory vaccine policies.