NB/ Germ theory led to a number of important breakthroughs in vaccinations in the 19^th century - perhaps most importantly Pasteur was able to prove how the technique of vaccination worked and Koch was able to establish a progress of isolating individual bacteria enabling vaccination to take off.
 
However as the timeline below shows most progress was made in the twentieth century.
 

 18th century

1798 First vaccine for smallpox, first vaccine for any disease developed by Edward Jenner.

 19th century

• 1879 First vaccine for cholera
• 1885 First vaccine for rabies
• 1890 First vaccine for tetanus
• 1896 First vaccine for typhoid fever
• 1897 First vaccine for bubonic plague

 20th century

• 1921 First vaccine for diphtheria
• 1926 First vaccine for pertussis (whooping cough)
• 1927 First vaccine for tuberculosis
• 1932 First vaccine for yellow fever
• 1937 First vaccine for typhus
• 1945 First vaccine for influenza
• 1952 First vaccine for polio
• 1954 First vaccine for Japanese encephalitis
• 1954 First vaccine for anthrax
• 1957 First vaccine for adenovirus-4 and 7
• 1962 First oral polio vaccine
• 1963 First vaccine for measles
• 1967 First vaccine for mumps
• 1970 First vaccine for rubella
• 1974 First vaccine for chicken pox
• 1977 First vaccine for pneumonia (Streptococcus pneumoniae)
• 1978