Rigel IV was the inhabited fourth planet of the Rigel system, in the Alpha Quadrant less than ninety light years away from Earth. (ENT: "Two Days and Two Nights") The system was affiliated with the United Federation of Planets. The planet was the homeworld of the Hill People and had deposits of boridium and murinite. (TOS: "Wolf in the Fold")
In 2266, the Redjac entity possessed Hengist, a native of Rigel IV, and killed several women on the planet. He was never caught and was only known as "Beratis". On Argelius II, Redjac committed a murder with a knife from Rigel IV's Argus River region. (TOS: "Wolf in the Fold")
In the 24th century, a brilliant astronomer with a fondness for the Betazoid Ambassador Lwaxana Troi resided on Rigel IV. He named a star after Lwaxana, or so she claimed in 2367. (TNG: "Half a Life")
Rigel IV was also the site of a pergium refinery. During the Dominion War, a shipment of pergium en route to Rigel IV from the Sappora system had been destroyed by the Jem'Hadar. (DS9: "Prodigal Daughter")
A question, which was not seen on screen, from Spock's memory test in Star Trek IV: The Voyage Home established that Rigel IV at one point signed a peace treaty with Argus. The treaty was important because it set a legal precedent that, All beings may not be created equal yet shall be given equal opportunity and treatment under the law. 
According to Star Trek: Star Charts (pgs. 52, 59, "United Federation of Planets I"), Rigel IV, also known as Beta Rigel IV was a M-class planet. The planet was a member planet of both the United Rigel Colonies and the United Federation of Planets. Rigel IV was admitted, along with the United Rigel Colonies, to the Federation in 2202.