This page contains information regarding Star Trek: Discovery, and thus may contain spoilers.
Aldebaran, also known as Alpha Tauri, was an inhabited planetary system in the Alpha Quadrant. This system was located near the Ficus sector. (TNG: "Contagion"; TNG-R: "Up The Long Ladder", okudagram)
In 2293, the location of Aldebaran in the Milky Way Galaxy was labeled on the star chart The Explored Galaxy, which was seen in James T. Kirk's quarters aboard the USS Enterprise-A. (Star Trek VI: The Undiscovered Country, okudagram)
In 2399, the location of Aldebaran was labeled on a star chart that was in Fleet Admiral Kirsten Clancy's office at Starfleet Headquarters. This system was in or near to Federation space. (PIC: "Maps and Legends")
It was the home system of such non-sentient animal life as the Aldebaran mud leech, the Aldebaran serpent, and the Aldebaran shellmouth. (TOS: "Amok Time", "The Deadly Years"; TNG: "Hide and Q"; ENT: "Anomaly")
In 2135, the HMS New Zealand was launched from Earth on a diplomatic mission to this system. It was listed on the chart Interstellar Expeditions to Sectors 184/02-185/38: Launched From Sol System, Earth Dates 2123-2190, which was seen on a screen in Jean-Luc Picard's ready room aboard the USS Enterprise-D. (TNG-R: "Up The Long Ladder", okudagram) The system was inhabited by Humans by the 23rd century.
During the 2260s, Janet and Theodore Wallace performed experiments using various carbohydrate compounds to slow down the degeneration of plant life at a Federation outpost on Aldebaran III. (TOS: "The Deadly Years")
For the remastered episode "Up The Long Ladder", Aldebaran replaced Alderaan.
In the Star Trek: Star Charts (p. 62) and Stellar Cartography: The Starfleet Reference Library ("Federation Historical Highlights, 2161-2385"), Aldebaran (Alpha Tauri) is a multi-star system with a trio of K-class stars and one M-class star. In 2385, this is a UFP system.
In the first draft script of ENT: "Strange New World", Travis Mayweather told a ghost story about a brain-sucking carnivore on a planet in the "Aldeberan system", though T'Pol refuted the tale, saying there were no such lifeforms in that system. During the episode's development, this ghost story instead became one about George Webb.