The Azure Quadrant

VOLTRON: The Denubian Galaxy

The Diamond System *

ARUS - Home of the VOLTRON FORCE. Ruled by Princess Allura.
AMPHROSE - Arus' "sister planet," where Judge Armistice marries Tilbar of Caspia and Marib of Noove before Lotor kidnaps him in hopes of marrying Allura. This takes place in the V3D episode, "Bride of the Monster." As with Pollux, "sister planet" is a comparative term (similar types of planets) and not an astronomical term.
POLLUX - Once known in history as Arus' "evil twin world." Ruled by Crown Prince Bandor and his older sister Princess Romelle. Helping them defend the planet is ex-Voltron Force member Sven. Romelle has used the term "sister planet" once to describe Pollux, but more than likely that was in the sense similar to "sister cities," in regards to their shared history and bloodlines. They are probably planets in adjacent orbits.
NORN* - Home to the legendary Muses of Norn. Planet where Bandor was taken hostage and Voltron was saved by King Alfor's Eclipse.
SHAMARA* - Not much is known about this planet, except that it's third moon is named Cryo. Allura crashed there and was rescued by the Garrett clone.

The Amethyst System *

LYRA* - The planet where the Roses of Lyra grow, which were needed to make an antidote to save Allura and others from the effect of poisonous flowers.
ZAUL - A mysterious desert planet that looks uninhabited on the surface, but underground live refugees in the ancient cities of the Darians.

The Turquoise System *

OLION* - A planet of the Galaxy Alliance whose representative was supposed to be attending a summit on Planet Arus, but had heard warning of a possible assassination, so clones were sent to be killed.
CYVILLE* - Only mentioned in the series when Allura mentions they must retrieve a trunk of jewels to get special medicine from planet Cyville to save her people. In my own writing, I have also attributed it to be the planet Hunk's orphan friends are from.

The Diadem System

GEO - the planet where the Voltron Force is sent as punishment for going against Amalgamus' orders in the V3D episode "A Rift In The Force." The Voltron Force must contend with mutated space lice and get back to Planet Arus in time to save it from invasion. Later, in the episode "Dominus," Geo has become so radioactive its uninhabitable, and also proves to be an excellent breeding ground for the title character of the episode. Dominus devours Geo's moon on one of its feeding sprees.
VERMILLION - the planet Hunk wants to go to and get supplies from in the V3D episode "Shades of Gray" before Haggar turns him into the Gray Lion. Star System isn't mentioned, but since it's another V3D planet, thought I'd put it here.
NOOB - the planet that Marib, the bride in the wedding ceremony at the opening of the V3D episode "Bride of the Monster," is from. Not to be confused with the ice planet Neeve from the original series. Since it's another V3D planet, I put it here. (In doing the work on the official visual starmap, I learned that NOOB was actually how Sean Catherine Derek spelled the planet name. And as accuracy has always been high on my list, the spelling is changed here and on the visual map.)