Back in the 80's and 90's Yoda was thought to be a member of The Whills
, but it is still not certain if The Whills are an organization of lorekeepers or the name of a race as a whole.
Yoda has been mistakenly been categorized as Lannik
, this is clearely an error.
The three known members of Yoda's species are Yoda, Yaddle and Vandar Tokare from the original Knights of the Old Republic game by Bioware. All three were Jedi Masters who sat on the Jedi Council in their respective eras. All three have been said to be wise, extremely powerful Force users and to have wielded green lightsabers.
I for one doubt, and hope Yoda's race will remain a Star Wars mystery.
BEHIND THE SCENES
For reasons unknown, George Lucas maintains a strict policy of keeping the history, name, origin, and whereabouts of this species secret. This policy has resulted even in certain Star Wars publications being canceled. A significant example of this policy was when Lucasfilm (likely at the direction of George Lucas himself) ordered the pulping of the entire print run of a yet-to-be-released Star Wars trading card depicting a group of the unknown tridactyl species worshipping a larger-than-life-size statue of one of their number, led in prayer by an individual who may have been intended to be Yoda.