While there are many historical lists of birthstones, the following table provides the two most common list. The center column give the historical list based on the Bible. The second is the more familiar, and currently used list. It was formalized in 1952. by the US Jewelry Industry Council. It is not based on the natural cycle of life on this planet, It is somewhat based on tradition, but only loosely.In 1912, in an effort to standardize birthstones, the (American) National Association of Jewelers met in Kansas and officially adopted a list. The Jewelry Industry Council of America updated the list in 1952 by adding alexandrite to June and citrine to November; specifying pink tourmaline for October; replacing December's lapis with zircon; and switching the primary/alternate gems in March. The most recent change occurred in October 2002, with the addition of tanzanite as a December birthstone. Britain's National Association of Goldsmiths created their own standardized list of birthstones in 1937.
There is a great introduction to Traditional Birthstones here - worth a look.
Aquamarine or Bloodstone
Pearl, or Moonstone
Peridot or Sardonyx