Most people believe that Conflict of Interest King Andrew Wakefield launched the anti-vaccination movement with his infamous Lancet article which described a purported relationship between vaccines and autism. However, the anti-vaccination movement is almost as old as vaccines themselves.
The earliest vaccinations, then called variolation, were to protect against smallpox and involved a patient being infected with the related (but less dangerous) cowpox. The technique was crude, but mostly effective. By the mid-1800's, attenuated vaccines replaced variolations, and in 1840 the English government made them mandatory. This led to public outrage and the arguments used against them back then are almost indistinguishable from those used today.
One notable critic is famed Evolutionary biologist Alfred Wallace, who was vehemently anti-vax. He said at the time "every day the vaccination laws remain in force parents are being punished, infants are being killed".
The fight over vaccines is nothing new, and you can read a more complete story on the history over The Atlantic in an excellent piece by author Elizabeth Earl.