The true beginning of stem cell research in sometimes in contention, as initial discoveries that led to todays research can be dated back as far as the 1800's.
That said, our modern understanding of stem cells begun in the 1950's, when researchers first discovered the presence of two different types in bone marrow; hematopoietic stem cells that are able to generate any type of blood cell, and stromal stem cells which form bone, fat and other cells in the body. Ongoing research led those initial discoveries to bone marrow transplants, the first of which were first sucessfully performed on fraternal twins.
It was in the mid-1970's that these stem cells were first found and reported in umbilical cord blood.
This discovery led to new research, and in the early 1980's it was found that cord blood stem cells were similar to those found in bone marrow and could be used as an alternative for transplants.
The first successful cord blood transplant was performed in 1988 in France, on a young boy suffering from Anemia (a blood disorder). Since then, ongoing research has led to the development of stem cell treatments being used today for almost 70 life-threatenting diseases.
In 2005 the United States congress passed the "Stem Cell Research and Therapeutic Act of 2005 (H.R. 2520)", national legislation that created new public banking and research facilities, as well as encouraged medical practicioners to increase awareness of cord blood donations to pregnant women.
Reseach in stem cell use continues, and most researchers agree that all of it's potential has yet to be discovered.