In 2267, Pluto's orbit was depicted on "Chart 14A: The Sol System". This chart was stored in the USS Enterprise library computer. The chart was scanned by the probe Nomad in auxiliary control. (TOS: "The Changeling" production art)
In 2152, Sub-Commander T'Pol compared the threat posed by the Andorians on Paan Mokar to Vulcan, with the menace a hypothetical Klingon military base on Pluto would represent to Earth. (ENT: "Cease Fire")
When using the slingshot effect to return to the 23rd century after the USS Enterprise had been hurtled through space to Earth and back in time to the year 1969, the ship engaged full braking power shortly after passing Pluto. (TOS: "Tomorrow is Yesterday")
In 2293, the maiden voyage of the USS Enterprise-B was planned as a "quick run around the block", taking the ship out beyond Pluto and then returning to spacedock. However, the flight plan was abandoned when the Enterprise received a distress call from the SS Lakul. (Star Trek Generations)
|The Sol System|
|Mercury • Venus • Earth (Luna) • Mars (Deimos) • Asteroid belt • Jupiter (Io; Ganymede) • Saturn (Mimas; Rhea; Titan) • Uranus • Neptune (Triton) • Pluto|
Discovered in the 20th century, Pluto was named for the god of the underworld in Roman and Greek mythology. Pluto was previously considered a planet until a series (2006, 2008) of controversial decisions of the International Astronomical Union reclassified the body as a dwarf or minor planet, and then later as a Plutoid as well.
Astrophysicist and cosmologist Neil deGrasse Tyson had actually already actively argued for the original reclassification, and his opinions weighed in heavily on the ultimate decision. What he had underestimated however, was the emotional attachment people, especially children, had for the "runt of the litter", and it was Tyson in particular who was singled out as proxy for criticism and hate mail and losing for the time being part of the goodwill he had accrued as science communicator. (The Colbert Report, 17 August 2006) Tyson had to answer for this again in the popular Star Trek friendly sitcom The Big Bang Theory when he made his guest appearance in the aptly titled 2010 season four episode "The Apology Insufficiency", aptly because it referred to Tyson's part in the demotion. And indeed, the US states New Mexico and Illinois had both already passed state laws by then, counteracting the demotion by ordaining Pluto as a bonafide planet in 2007   and 2009 respectively.  These reclassifications have, to date, never been mentioned in Star Trek itself. 
The Star Trek Encyclopedia (4th ed., vol. 2, p. 172) described Pluto as a minor planet.
In the first draft script of ENT: "Strange New World", Charles Tucker told a ghost story about a Tellarite transport which had crash landed on Pluto, a few years previously. In the final version of the episode, though, this was replaced with Tucker commenting, "Has anyone heard the one about the haunted comet?"
According to the Spaceflight Chronology, the first Pluto Base began operation in the year 2039 as a navigational check point for extra-solar missions. According to The Worlds of the Federation (p. 12), Pluto was the site of the Pluto Research Base, where all life was decimated by a strain of the omega virus, some time after the founding of the Federation. According to Star Trek: Star Charts (Pgs.39, 62, "United Federation of Planets I"), Pluto was classified as a C-class planet. The planet was a charter member of the United Federation of Planets in 2161. Once considered "official", these works have been demoted to apocrypha status by the franchise as of March 2002. (Star Trek: The Magazine Volume 2, Issue 11, p. 71)
In the novel Before Dishonor, Pluto was "absorbed" by the evolved Borg, who literally devoured the planet and its associated satellites en route to attacking Earth. Characters mention the controversy about its status, mentioning that it had switched back and forth several times. Upon its destruction, one of the characters sardonically comments that at least this would settle the controversy.
Star Trek Online established that the Sol system has eight planets in the system's description. Pluto, alongside the unnamed planet which Starbase 1 orbits, are still visible in in-game astrometric depictions of the Sol system, indicating that both worlds are considered dwarf planets in the 2250s and 2400s.