The modern Birthstone list contains the official birthstone list from the American National Association of Jewelers, Jewelers of America. These gemstones were officially adopted in 1912. In the US, this is the accepted list.
Listed are the months and their modern birthstone
January – Garnet
February – Amethyst
March – Aquamarine or Bloodstone
April – Diamond
May – Emerald
June – Pearl, Moonstone, Alexandrite
July – Ruby
August – Peridot, Sardonyx, Spinel
September – Sapphire
October – Opal, Tourmaline
November – Topaz or Citrine
December – Tanzanite, Turquoise, Zircon, Blue Topaz
Apart from the modern birthstones there are other birthstones like the traditional birthstones, mystical birthstones and ayurvedic birthstones.
The Star Sign stone chart below offers another slant on birthstones/planetary relationships.
Sun Signs and their respective birthstones:
Capricorn (Dec. 22 – Jan. 19) – Ruby,Agate, Garnet
Aquarius (Jan. 20 – Feb. 18 ) – Garnet, Moss Agate, Opal, Amethyst
Pisces (Feb. 19 – Mar. 20) – Rock Crystal, Sapphire, Amethyst, Bloodstone
Aries (Mar. 21 – Apr. 19) – Bloodstone, Diamond
Taurus (Apr. 20 – May 20) – Sapphire, Turquoise, Amber, Blood Coral, Emerald
Gemini (May 21 – Jun. 20) – Agate, Chrysoprase, Pearl
Cancer(Jun. 21 – Jul. 22) – Emerald, Moonstone, Pearl, Ruby
Leo (Jul. 23 – Aug. 22) – Tourmaline, Sardonyx, Onyx
Virgo (Aug. 23 – Sep. 22) – Jasper, Carnelian, Jade, Sapphire
Libra (Sep. 23 – Oct. 22) – Opal, Lapis Lazuli, Peridot
Scorpio (Oct. 23 – Nov. 21) – Aquamarine, Topaz
Sagittarius (Nov. 22 – Dec. 21) – Sapphire, Amethyst, Turquoise, Topaz