Aldebaran, also known as Alpha Tauri, was the primary of its star system, in the Alpha Quadrant. This star's system was located near the Ficus sector. (TNG: "Contagion"; TNG-R: "Up The Long Ladder", okudagram)
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 Aldebaran's 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) Aldebaran's star 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")
In 2293, the location of Aldebaran in the Milky Way Galaxy was labeled in 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)
For the remastered episode "Up The Long Ladder", Aldebaran replaced Alderaan.
According to 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 was 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.