The scientific basis for current medical practice was developed during the 19th century, and all of the disciplines--except anatomy--that make up the first two years of medical school were founded. 

Jakob Henle linked the study of anatomy with the study of biological functions and created physiology.  Robert Virchow created the field of cellular pathology.  Louis Pasteur's experiments, including his famous study of hydrophobia-rabies, evolved into the field of microbiology, and when Robert Koch discovered the bacteria that created anthrax, tuberculosis, and cholera, he created the field of bacteriology. 
 
Advances in clinical medicine did not advance as rapidly as basic medical science.  There were, however some dramatic discoveries.  Joseph Lister proved that surgery could be made safer by disinfecting surgical equipment, and William Morton developed anesthesia techniques that made surgery painless. 

If you would like to learn more more about 19th Century Medicine the Karolinska Institute has some interesting links.  (Scroll down the Karolinska page until you come to the 19th Century section.)