The races within Final Fantasy XIV are the same ones that are in Final Fantasy XI, but with different names. This was done so that the players would have a familiar feel to the game. However this does not rule out additional races that were not in Final Fantasy XI. So far no new ones have been announced.
Hyur

The Hyur race has the highest population within the region of Eorzea; where they migrated in three waves. With them they brought advanced technology and rapidly became a driving force behind cultural progress. The Hyur were known as the Hume race in Final Fantasy XI.
Elezen

The Elezen race were the first race to exist in the lands of Eorzea and have adapted to their environment by becoming taller and evolving more sensitive ears. Throughout the history of the Elezen race they have fought wars with the Hyurs as they believed their migration to their lands was an invasion. However they now live peacefully together. The Elezen were known as the Elvaan race in Final Fantasy XI.
Lalafell

The Lalafell migrated to Eorzea from the islands of the south when trade routes began to spring up. Being short gives them increbile agility and they are said to be an intelligent race. Th Lalafell were known as the Tarutaru race in Final Fantasy XI.
Roegadyn

The Roegadyn are a maritime race who are mostly found in the northern seas. They are a very muscular race and are known for the cultural emphasis they place on competition and courage. In Final Fantasy XI the Roegadyn were known as the Galka race, however in Final Fantasy XIV they do not have a tail.
Miqo'te

The Miqo'te race migrated to Eorzea during the Age of Endless Frost when the seas turned to ice and allowed them to cross. Since then, they have separated into two physically distinguishable groups known as the Diurnal Seekers of the Sun and the Nocturnal Keepers of the Moon. The Miqo'te are few in number within Eorzea and prefer to live isolated lifestyled, avoiding contact with the other races. The Miqo'te were known as the Mithra race in Final Fantasy XI.