There are so many medical advances made by animal testing that I could not go into detail about all of them.  I have made a time line about the most important and and went in dept about very important discoveries.

Before the 20th Century

Malaria parasite lifecycle (cows, pigeon)
Smallpox vaccine in 1796 by Edward Jenner (cows)
Vaccine for anthrax by Louis Pasteur in 1881(sheep)
Rabies vaccine by Louis Pasteur and Emile Roux in 1885 (rabbits, dogs)
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Edward Jenner

Insulin (1922)

        In 1922, diabetes was a death sentence.  No treatment was available and very little was known about it except that sugar worsened patients condition.
        Fredrick Banting had a revolutionary idea.  He already knew that islets of Langerhans (part of the pancreas)  and diabetes had a close relationship.  Earlier in the century, many had tried unsuccessfully to take the ingredient out of the islets of Langerhans.  Banting's idea was that the digestive juice of the pancreas were destroying the islets before what they needed could be isolated.  Banting also knew that if he could stop the pancreas from producing juices but keep the islet of Langerhans working, the 'stuff' they were looking for would present itself.  Another fellow research John Macleod did not believe Banting's theory but eventually gave him a lab, an assistant named Charles Best, and some test dogs.  In May of 1922, the experiments began and by August results were already discovered.  Banting and his assistant successfully isolated the material from the islet of Langerhans (insulin) and injected it into their diabetic dogs; this lowered their high blood sugar.  Though Banting had some trouble getting the insulin to the right purity and strength, eventually it was safe enough to test on humans. Their test subject was a young boy dying of diabetes.  When giving the insulin his blood sugar lowered and many other symptoms of his diabetes disappeared. 
        Banting and Macleod were awarded the Nobel Prize for their discovery.  Today it is estimated 15 million people are alive because of this discovery.
 
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On the left is Charles best. To the right is Fredrick Banting. The dog in the middle was one of the several diabetic dogs they used.

1930's

Modern anaesthetics (rats, rabbits, dogs, cats, monkeys)
Tetanus vaccine (horses, guinea pigs)
Anticoagulants (rabbits, guinea pigs, mice, dogs)

Penicillin (1940)

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Alexander Fleming
        In 1928, Alexander Fleming was conducting as experiment with the bacteria staphylococcus bacilli.  His petri dish was contaminated with a type of mold called Pencillim notatum.  The places where the mold was the bacteria did not grow.  This led to the discovery of what is now known all over the world as Penicillin.
           It was not until 1940 that pencillin was really tested.  Up until that point not much attention had been paid to it and not enough of it had been collect yet to do tests.  Howard Florey's experiment involved eight rats, all of them injected with a deadly dose of staphylococcus bacilli. Later that day four of the eight rat were given penicillin and all lived.  Those who were not given penicillin died as was expected.  Florey said "it looks like a miracle". 
        He was right penicillin was a miracle to many suffering with bacterial diseases that could now be cured.  

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1940's

Kidney dialysis by Dr. Willem Kolff in 1943 (guinea pigs, rabbits, dogs, monkeys)
Whooping cough vaccine by Pearl Kendrick in 1942 (mice, rabbits)

1950's

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1953 Heart-lung Machine
Heart-lung machine for open heart surgery. First successful surgery was in 1953 by John Gibson (dogs)
Hip replacement surgery (dogs, sheep, goats)
Cardiac pacemakers (dogs) First usable design by Earl Bakken in 1958.
Medicines for high blood pressure (rats, mice, dogs)
Replacement heart valves (dogs, calves, rabbits, guinea pigs, rats)

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First successful pacemaker

Polio Vaccine (1952)

        Polio is a infectious virus that targets nerves in the body, this can lead to paralysis and is often fatal.  Jonas Salk, head of the Virus Research Lab at Pittsburgh University, started studying the polio virus in 1947.  In 1948, researchers at Harvard University discovered a way to grow polio and other diseases on scraps of tissue in large quantities for research purposes; this discovery greatly sped up Salk's research. In 1952, Salk successfully weakened the virus enough so as it wouldn't hurt the body but would still raise antibody levels.  After the discovery was proven to work, all school children in America were vaccinated starting in 1954.  By 1955 four million vaccine had been given out.  The amazing affects of Salk vaccine can be seen in the statistics: In 1955 there were 28,985 cases of polio; in 1956, 14,647; in 1957, 5,894. By 1959, 90 other countries used Salk's vaccine.  The vaccine had almost eliminated polio. 
        Later on, researcher Albert Sabin improved Salks vaccine by making it a live vaccine.  This made the vaccine stronger, the process of making it cheaper, and the way of receiving it easier (orally).  Sabin's experiments included hundreds of experiments on monkeys. 
        "It (Salk's vaccine) gave ushope and peace of mind. It made theworld safe again for most children. No more fear of iron lungs, death, orbeing 'crippled," Nancy Leyerzaf, polio pioneer.

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Kidney Transplant (1953)

        Joesph E. Murray develop kidney transplant techniques while working on pigs and dogs through out the 1950's.  Soon human patients were getting the operation but a flaw still remained: many patients new kidneys were 'rejected' by their body.  Basically,  if the kidney was not a perfect match, the body would see it as a foreign object and attack it. In 1972, Cyclosporine was discovered.  It was tested on rats and was shown to suppress the immune system.  Animal testing was necessary in the development of the kidney transplant because although they had tissue cultures and other alternatives a full circulatory system is needed to get accurate results.Kidney transplant tests in dogs proved that with the combination of Cyclosporine and steroids kidneys would be accepted in three times as many surgeries as before.  This proved to hold true and be applicable in humans also.

1960's

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Christiaan Barnard
Heart transplants by Christiaan Barnard in 1967 (dogs, monkeys)
Coronary bypass operations first successfully perfored by Dr. Robert Goetz in 1960(dogs)
Chemotherapy for leukaemia by Emil J. Freireich Jr. in 1962 (mice)
MRI scanning for improved diagnosis in 1974(rabbits, pigs)

1980's

Treatment for river blindness (a parasitic blindness disease) (rodents, cows)
Life support systems for premature babies (monkeys)
Hepatitis B vaccines by Maurice Hilleman in 1981 (monkeys)
Treatment for leprosy in 1981 (armadillos, monkeys)

1990's

Combined therapy for HIV infection (mice, monkeys)
Meningitis vaccines (mice)
Medicines for breast and prostate cancer (mice, rats, dogs)
Medicines for type 2 diabetes (mice)

2000's

Deep Brain Stimulation for Parkinson’s Disease in 2002(monkeys)
Cervical cancer vaccine in 2009(rabbits, cattle)
Bird flu vaccine (chickens and ferrets)