Hylian
Essentially a human. The only difference being the pointed ears and occassional ability to do magic. Traditionally, the ruling family of Hyrule is Hylian. Important note: Link is a Hylian, not a Kokiri, a common mistake.
A Sheikah
A very mysterious race of ninja like warriors. Sheikah are the sworn protectors of the Hylian throne. Very skilled in magic and combative arts.
Zora
A fishlike race that inhabit several body's of water in the Hyrule area. Renowned for their skills in medicine. These individuals are very well adapted to aquatic environments and a fiercely loyal to the Royal Family of Hyrule.Gerudo
Gerudos are a race of thieves that live in a desert fortress. This tribe is composed entirely of females except for a male that is born every 100 years to become their king. Gerudo's are very skilled archers and riders and are known for their stealth. Ganondorf himself is from this race.
Kokiri
This carefree race dwells in the Kokiri Forest. They look much like children and are terrified of the outside world. Each has a guardian fairy and they are closely watched by the Great Deku Tree, an ancient guardian spirit of the forest. Link was raised by the Kokiri which explains his fairy, Navi.
Goron
Gorons are a fierce but loveable. They dwell in underground caverns and enjoy a diet of rare rocks. Gorons are excellent metal smiths and tunnelers. They also have a soft spot for music. It's speculated that Goron's are hermaphroditic because it is impossible to tell male from female.