Rigel V is the fifth planet in the Rigel system, and homeworld of the vulcanoid Rigellians. (TOS: "Journey to Babel") It is a member of the United Rigel Colonies, and through that organization, the United Federation of Planets.
Although not canonically established, some assume that another star with a similar-sounding name exists much closer to Sol, thus explaining how the Enterprise (NX-01) could reach this star at all, or how planets orbiting Rigel could be out-of-reach (TOS: "Mudd's Women") and highly populated (TOS: "The Doomsday Machine") at the same time. Possibly, "Rigel" was sometimes referring to "Rigil Kentaurus," another name for Alpha Centauri. However, a hypothetical second Rigel created to cope with those problems is called Beta Rigel in the Star Trek: Star Charts.