(covers information from several alternate timelines)
At some point prior to 2268, the USS Enterprise, under the command of Captain James T. Kirk, engaged and defeated a Romulan vessel near Tau Ceti, using the Cochrane deceleration maneuver. (TOS: "Whom Gods Destroy")
In 2293, the location of Tau Ceti in the Milky Way Galaxy was labeled in a star chart that was in Captain James T. Kirk's quarters aboard the USS Enterprise-A. (Star Trek VI: The Undiscovered Country, production art)
In 2364, the location of Tau Ceti was labeled in a star chart of a stellar neighborhood with Sol at the center. This chart was stored in the USS Enterprise-D library computer. Later that year, the chart was scanned by Outpost 63. (TNG: "The Naked Now", production art; TNG: "The Last Outpost")
In 2155, in the mirror universe, Tau Ceti was the system in which the Terran Empire lost twelve ships in a battle against alien rebels. Propaganda had spread that this was a major victory for the Terran Empire, when in fact it was a sign they were losing. (ENT: "In a Mirror, Darkly")
Background information Edit
The chart naming stars within 20 light years of Sol was drawn by Rick Sternbach for the Star Trek Spaceflight Chronology in the late 1970s. Found on page 77, this chart showed Earth commercial and exploration routes after the use of warp drive began. Tau Ceti was the destination on an exploration route. According to the Spaceflight Chronology, the UNSS Bonaventure, under the command of Captain Hadrian Huckleby, began Earth's warp drive era with a trip to Tau Ceti four years after the first successful demonstration of warp technology.
According to The Worlds of the Federation, Tau Ceti III was the planet Kaferia, homeworld of the insectoid Kaferians. In TNG: "Where No One Has Gone Before" and TNG: "Remember Me", The Traveler was also said to be a native of Tau Alpha C, suggesting Tau Alpha C was located in the Tau Ceti system.
According to Star Trek: Star Charts (pg. 44), from the mid-22nd century, Tau Ceti was located in or near Federation space, in the Alpha Quadrant. The planet Kaferia was the third planet. Tau Ceti was a G-class star with a magnitude of +5, which was the same brightness as Sol.
According to the novel Enterprise: The First Adventure, Tau Ceti was located along the Romulan Neutral Zone and the inhabitants of Tau Ceti II were widely regarded as possessing great mineralogical expertise, using sapphires as the local currency.