Starbase 14
Facility that sent a message to the Enterprise-D in 2364 concerning the Anchilles fever outbreak on planet Styris IV.
  "Code of Honor" - TNG.
Starbase 23
Federation starbase, located very close to the Romulan Neutral Zone. Following her temporary removal from duty in 2369, Dr. Beverly Crusher was scheduled to arrive by shuttlecraft at Starbase 23. From there, she planned to take a transport to Earth. In the anti-time reality created by the Q Continuum, Captain Picard sent word to Starbase 23 to check their personnel for the effects of temporal reversion.
  "Suspicions" - TNG. "All Good Things..." - TNG.
Starbase 24
Starfleet facility near Khitomer. Young Worf's nursemaid, Kahlest, was taken there for treatment of her injuries following her rescue from Khitomer in 2346.
  "Sins of the Father" - TNG. "Redemption, Part I" - TNG.
Starbase 27
Facility to which Kirk was ordered to transport the surviving colonists from planet Omicron Ceti III in 2267.
  "This Side of Paradise" - TOS.
Starbase 36
The Enterprise-D was scheduled to stop at Starbase 36 in late 2367. Dr. Beverly Crusher suggested that Lieutenant Commander La Forge have his VISOR checked for malfunctions during the stopover there.
  "The Mind's Eye" - TNG.
Starbase 39-Sierra
Facility approximately 5 days' travel from the Romulan Neutral Zone.
  "The Neutral Zone" - TNG.
Starbase 41
Arjin traveled from Starbase 41 to station Deep Space 9 in order to meet his field docent, Lieutenant Commander Jadiza Dax, in 2370. He had met Dr. Julian Bashir on the transport from Starbase 41.
  "Playing God" - DS9.
Starbase 47
In an alternate quantum reality visited by Worf in 2370, Starbase 47 was the object of covert surveillance by the Cardassians, who had reprogrammed the Argus Array to observe the starbase, as well as other Federation installations.   "Parallels" - TNG.
Starbase 53
Federation station. In 2374, Section 31 operatives told Julian Bashir that he was to be taken to Starbase 53 for questioning.
  "Inquisition" - DS9.
Starbase 63
Worf and Dax visited Starbase 63 just prior to stardate 50416.
  "The Darkness and the Light" - DS9.
Starbase 67
Counselor Troi and La Forge were ordered by the Ktarians to travel to Starbase 67 to distribute the addictive Ktarian game to starships docked there.
  "The Game" - TNG.
Starbase 73
Facility at which the Enterprise-D received mission orders to investigate a distress signal detected from the Ficus Sector. Starbase 73 was commanded by Admiral Moore. Worf delivered his son, Alexander Rozhenko, to Starbase 73 in 2367. Worf's adoptive parents met them there, having agreed to accept custody of Alexander after the death of K'Ehleyr.
  "Up the Long Ladder" - TNG. "Reunion" - TNG.
Starbase 74
Massive orbital facility at planet Tarsas III. The Enterprise-D underwent a computer-systems upgrade there in 2364, although the operation was interrupted when a group of Bynar technicians attempted to hijack the ship to save their planet. Starbase 74 was commanded by Commander Orfil Quinteros.
Starbase 74 miniature shots were a partial re-use of some visual-effects elements originally shot for Star Trek III by ILM. However, it's been pointed out that Starbase 74 must be a substantially larger structure than Spacedock as seen in Star Trek III, since the Galaxy-class Enterprise-D is much larger ship than the original Constitution-class vessel. The shot of the Enterprise-D actually docked inside the station was a matte painting designed by Andrew Probert.   "11001001" - TNG.
Starbase 82
Site where the Enterprise-D delivered a Ktarian vessel into Starfleet custody in 2368.
  "The Game" - TNG.
Starbase 83
The Enterprise-D traveled to Starbase 83 when Q returned the ship to Federation space after first contact with the Borg Collective.
  "Q Who?" - TNG.
Starbase 84
Location where the Enterprise-D acquired a replacement warp core that had been infested by interphasic organisms. The core had been manufactured on the planet Thanatos VII, where the interphasic organisms were attracted to the new interphasic-fusion manufacturing process.
The Starbase 84 miniature was a re-use of the Spacedock, originally created for Star Trek III by ILM.
  "Phantasms" - TNG.
Starbase 87
Intended destination of the Enterprise-D following its departure from Boraal II.
  "Homeward" - TNG.
Starbase 97
Starfleet facility commanded by Admiral Mitchell. Commander Calvin Hutchinson served for some time there, prior to his assignment to Arkaria Base.
  "Starship Mine" - TNG.
Starbase 103
Facility located a short distance from planet Minos. After ordering a saucer separation maneuver at Minos, Geordi La Forge instructed Engineer Logan to proceed to Starbase 103.
Of course, even if Starbase 103 was only a few light-years from Minos, it's unclear as to what purpose there might of been in heading toward the base, since the saucer section had no warp-drive capabilty.
  "The Arsenal of Freedom" - TNG.
Starbase 105
Starfleet facility. In the alternate history created when the Enterprise-C vanished from its proper time in 2344, Starbase 105 was a possible destination to which the Enterprise-C could of been escorted.
  "Yesterday's Enterprise" - TNG.
Starbase 117
Site to which the Enterprise-D sent two members of the Ferengi Trade Mission, following their part in an accident that befell Kriosian Ambassador Briam in 2368.
  "The Perfect Mate" - TNG.