Aldebaran was the primary of the Aldebaran system containing at least three planets. The star was located in the Alpha Quadrant, located near the Ficus sector within at a distance of less then 90 light years of the Sol system. (ENT: "Two Days and Two Nights"; TNG: "Up The Long Ladder"; Star Trek VI: The Undiscovered Country production art)
In 2135, the HMS New Zealand was launched from Earth on a diplomatic mission to Aldebaran. (TNG: "Up The Long Ladder") In the 2260s, Janet and Theodore Wallace performed experiments using carbohydrate compounds to slow the aging of plants on a Federation outpost on Aldebaran III. (TOS: "The Deadly Years")
The Aldebaran mud leech, the Aldebaran serpent, Aldebaran whiskey, and the Aldebaran shellmouth originate from this system. It was also the location of the Aldebaran Music Academy in the 2340s. (ENT: "Anomaly"; TOS: "Amok Time"; TNG: "Hide and Q", "Relics"; DS9: "Prophet Motive", "Explorers", "Distant Voices", "Shadowplay")
According to ENT: "Two Days and Two Nights", prior to 2151, Earth ships had been operating within 90 light years of the Sol system. In that year, the Enterprise became the first ship to travel further than this distance. According to Startrek.com, Aldebaran (Alpha Tauri) was a spectral type K5 star located 68 light years from Sol. 
On "The Explored Galaxy" star chart "Aldebaran" was misspelled as "Aldeberan". Aldebaran was located between the Tholian Assembly and Romulus. Both locations were identified in DS9: "Call to Arms" as being in the Alpha Quadrant.
According to Star Trek: Star Charts (pg. 60), Aldebaran (Alpha Tauri) was a quadrinary star system. Aldebaran A was a K-class star with a magnitude of -1, which was a hundred times brighter than Sol. Aldebaran B and C were K-class stars and Aldebaran D was an M-class star.