This is a listing of ships that have been either mentioned on Star Trek, listed on an LCARS readout, or if they were seen, it's class was unidentified.

USS Aeon NCV-
   Small timeship from the 29th century commanded by Captain Braxton on a mission to destroy the USS Voyager NCC-74656. The Aeon    crash landed on Earth in 1967.
   "Future's End" - VOY.
USS Ahwahnee NCC-2048
   Potential participant in Operation Retrieve to rescue Captain Kirk and Dr. McCoy from Rura Penthe in 2293.
   "Star Trek VI: The Undiscovered Country"
USS Antares NCC-501
   Science vessel destroyed by Charles Evans in 2266.
   Named for the brightest star in the constellation Scorpius.
   "Charlie X" - TOS.
USS Archer NCC-44278
   Part of the fleet to rendezvous with the USS Enterprise NCC-1701-E to intercept the Reman warship Scimitar.
   Named for Enterprise NX-01 Captain Jonathan Archer.
   "Star Trek: Nemesis"
SS Artemis
   Departed in 2274 to transport colonists to Septimus Minor, but went off course and delivered the colonists to Tau Cygna V.
   "The Ensigns of Command" - TNG.
USS Baton Rouge NCC-
   Shown as part of a personnel file (Darien Wallace).
   "Eye of the Beholder" - TNG.
SS Beagle
   Commanded by Captain Merrick with crew of 47. In 2261, the Beagle was damaged by meteors and drifted towards Eight Ninety-Two-IV    where the crew was captured by the inhabitants.
   "Bread and Circuses" - TOS.
USS Beagle NCC-
   One of 39 starships lost at the battle of Wolf 359.
   - TNG.
USS Brahe NCC-
   One of 39 starships lost at the battle of Wolf 359.
   - TNG.
USS Carolina NCC-
   In 2377, under the command of Captain Peterson sent to intercept a Ferengi ship from luring Voyager into a trap.
   "Inside Man" - VOY.
USS Challenger NCC-2032
   Potential participant in Operation Retrieve to rescue Captain Kirk and Dr. McCoy from Rura Penthe in 2293.
   Named in honor of the space shuttle Challenger that was destroyed in 1986 killing all of it's crew.
   "Star Trek VI: The Undiscovered Country"
USS Chicago NCC-
   Shown as part of a personnel file (Walter J. Pierce).
   "Eye of the Beholder" - TNG.
USS Clavyn NCC-
   Shown as part of a personnel file (Anaanda Ziff).
   "Eye of the Beholder" - TNG.
USS Columbia NCC-621
   Ordered to rendezvous with the USS Revere by Commodore Probert in 2271.
   "Star Trek: The Motion Picture"
SS Columbia
   Federation science vessel that made a forced landing on Talos IV in 2254.
   "The Cage" - TOS. "The Menagerie" - TOS.
USS Cortéz NCC-
   Part of Operation: Return to retake Deep Space 9 during the Dominion War in 2374. Shortly after the retaking of DS9 the Cortéz was    lost and presumed destroyed.
   Named after Hernan Cortéz, the Spanish conquistador who overthrew the Aztec empire and won Mexico for the crown of Spain.
   "Sacrifice of Angels" - DS9. "Far Beyond the Stars" - DS9.
USS Destiny NCC-
   While on an assignment to transport the Dax symbiont to Trill in 2374 it required an emergency transplant to survive into Erzi Tigan.    The Destiny returned to DS9 before rejoining the Seventh Fleet however Ezri Dax decided to stay on DS-9 instead.
   Named after the United States' scientific lab module for International Space Station.
   "Shadows and Symbols" - DS9. "Afterimage" - DS9.
SS Dierdre
   Used by the Klingons in a hoax signal to the USS Enterprise NCC-1701 in 2268.
   "Friday's Child" - TOS.
USS Elkins NCC-74121
   Intrepid-class variant.
   Named after Judy Elkins, DS9 visual effects coordinator.
   The DS9TM Kitbashes (EAS).
   "A Time to Stand" - DS9.
USS Emden NCC-1856
   Potential participant in Operation Retrieve to rescue Captain Kirk and Dr. McCoy from Rura Penthe in 2293.
   "Star Trek VI: The Undiscovered Country"
USS Entente NCC-2120
   Mentioned in the radio chatter the Epsilon IX monitoring station.
   "Star Trek: The Motion Picture"
USS Esteban NCC-
   One of 39 starships lost at the battle of Wolf 359.
   - TNG.
USS Everest NCC-
   One of 39 starships lost at the battle of Wolf 359.
   - TNG.
USS Falcon NCC-
   One of 39 starships lost at the battle of Wolf 359.
   - TNG.
USS Gallico NCC-
   Shown on DS9 vessel arrival list.
   "Whispers" - DS9.
USS Gauss NCC-
   One of 39 starships lost at the battle of Wolf 359.
   - TNG.
USS Gemine NCC-
   One of 39 starships lost at the battle of Wolf 359.
   - TNG.
USS Gettysburg NCC-
   Docked at DS9 in 2375 for maintenance.
   The Star Trek Encyclopedia implies this is the same Constellation-class ship from TNG which is possible, however unlikely.
   "Treachery, Faith, and the Great River" - DS9.
USS Hauck NCC-
   Conducted a test flight with the USS Voyager in 2371.
   Star Trek: The Magazine.
USS Helin NCC-1692
   Potential participant in Operation Retrieve to rescue Captain Kirk and Dr. McCoy from Rura Penthe in 2293.
   "Star Trek VI: The Undiscovered Country"
USS Hispanola NCC-
   Shown on DS9 vessel arrival list.
   "Whispers" - DS9.
USS John F. Kennedy NCC-
   Shown on a display screen.
   "Conspiracy" - TNG.
USS John Muir NCC-1732
   Potential participant in Operation Retrieve to rescue Captain Kirk and Dr. McCoy from Rura Penthe in 2293.
   "Star Trek VI: The Undiscovered Country"
USS Khuma NCC-
   One of 39 starships lost at the battle of Wolf 359.
   - TNG.
USS Klondike NCC-
   One of 39 starships lost at the battle of Wolf 359.
   - TNG.
USS Kobayashi Maru NCC-
   Class 3 neutronic fuel carrier.
   "Star Trek II: The Wrath of Khan"
USS Korolev NCC-2014
   Shown on a display screen.
   "Star Trek VI: The Undiscovered Country"
USS Liberator NCC-67016
   Destroyed by the Borg in 2367.
   The name and registry comes from a damaged shuttle from The Art of Star Trek.
   "The Best of Both Worlds" - TNG.
USS Macau NCC-
   One of 39 starships lost at the battle of Wolf 359.
   - TNG.
USS Malone NCC-
   Shown as part of a personnel file (Anaanda Ziff).
   "Eye of the Beholder" - TNG.
USS Manson NCC-
   Fought the Borg in Sector 001 in 2372.
   Overheard in radio chatter.
   "Star Trek: First Contact"
USS Mayflower NCC-
   Seen in signage label on DS9 in the Encyclopedia.
USS Maxwell NCC-
   One of 39 starships lost at the battle of Wolf 359.
   - TNG.
USS Milan NDT-50863
   Transport ship used by Helena and Alexander Rozhenko to travel to the Enterprise-D from Earth in 2368.
   "New Ground" - TNG.
USS Musashi NCC-
   Docked at DS9 in 2375.
   Named for the Japanese dreadnaught that sunk in the Sibuyan Sea in 1944.
   "Treachery, Faith, and the Great River" - DS9.
USS Nepal NCC-
   One of 39 starships lost at the battle of Wolf 359.
   - TNG.
USS Neptune NCC-
   One of 39 starships lost at the battle of Wolf 359.
   - TNG.
USS Niels Bohr NCC-
   Shown as part of a personnel file (Bruno Salvatore).
   "Eye of the Beholder" - TNG.
USS Northridge NCC-
   Shown as part of a personnel file (Lois A. Eckridge).
   "Eye of the Beholder" - TNG.
SS Odin NGL-12535
   Freighter craft disabled near Angel One in 2357.
   Named for the Norse God.
   "Angel One" - TNG.
USS Olympia NCC-
   Commanded by Captain Lisa Cusak conducting an eight-year deep space exploration mission in the Beta Quadrant from 2363 to 2371.    Destroyed while investigating a planet by a quantum reaction in an exogenic energy field causing a surge of metreon radiation. The   Olympia was discovered by the USS Defiant NX-74205 in 2374.
   Named for the region in western Peloponnesus, the site of the first Olympic games.
   "The Sound of Her Voice" - TNG.
USS Oregon NCC-
   Shown on DS9 vessel arrival list.
   "Whispers" - DS9.
USS Peking NCC-
   One of 39 starships lost at the battle of Wolf 359.
   - TNG.
USS Peterson NCC-
   Shown as part of a personnel file (Anaanda Ziff).
   "Eye of the Beholder" - TNG.
USS Philadelphia NCC-
   Shown as part of a personnel file (Alfonse D. Pacelli).
   "Eye of the Beholder" - TNG.
USS Pioneer NCC-
   One of 39 starships lost at the battle of Wolf 359.
   - TNG.
USS Popovich NCC-
   One of 39 starships lost at the battle of Wolf 359.
   - TNG.
USS Pueblo NCC-
   One of 39 starships lost at the battle of Wolf 359.
   Shown as part of a personnel file (Daniel L. Kwan).
   "Eye of the Beholder" - TNG.
USS Raven NAR-32450
   The Raven was a privately owned vessel in a science mission to investigate rumors of the Borg in 2354. The crew consisting of Magnus     and Erin Hansen and their daughter Annika, were assimilated by the Borg.
   When the Raven was first seen it had the registry prefix NAR, but was later changed to a NCC prefix.
   "The Raven" - VOY. "Dark Frontier" - VOY.
USS Republic NCC-
   A 50 year old cadet training ship.
   While it is unlikely that the Republic is the same Constitution-class ship from TOS, writer Ronald Moore indicated it probably was.
   "Valiant" - DS9.
USS Revere NCC-595
   Mentioned in the radio chatter the Epsilon IX monitoring station.
   "Star Trek: The Motion Picture"
USS Rixx NCC-
   One of 39 starships lost at the battle of Wolf 359.
   - TNG.
USS Saratoga NCC-
   Docked at DS9 in 2374.
   "Wrongs Darker Than Death or Night" - DS9.
USS Sarek NCC-
   Part of the task force to retake DS9 during the Dominion War in 2374.
   Named after the famous Vulcan ambassador.
   "Favor the Bold" - DS9.
USS Scovil NCC-1598
   Potential participant in Operation Retrieve to rescue Captain Kirk and Dr. McCoy from Rura Penthe in 2293.
   "Star Trek VI: The Undiscovered Country"
SS Seattle NAR18834
   Launched in 2120 under the command of Wendy Neuss on an ADR looping mission of the Ficus sector.
   Listed on a LCARS in-joke.
   "Up the Long Ladder" - TNG.
USS Seaquest NCC-
   Shown as part of a personnel file (Darien Wallace).
   "Eye of the Beholder" - TNG.
USS Seaview NCC-
   Shown as part of a personnel file (Daniel L. Kwan).
   "Eye of the Beholder" - TNG.
USS Sentinel NCC-
   Docked at DS9 in 2375.
   "Treachery, Faith, and the Great River" - DS9.
USS Shepard NCC-
   Disabled by an unknown alien probe heading for Earth in 2286.
   "Star Trek IV: The Voyage Home"
USS Shika Maru NCC-
   Encountered a Tamarian vessel in the 23rd century.
   "Darmok" - TNG.
USS Shimour NCC-
   One of 39 starships lost at the battle of Wolf 359.
   - TNG.
USS Silversides NCC-
   Shown as part of a personnel file (Marla E. Finn).
   "Eye of the Beholder" - TNG.
USS Solaris NCC-
   One of 39 starships lost at the battle of Wolf 359.
   - TNG.
USS Springfield NCC-1963
   Possible participant in the mission to rescue Captain Kirk and Doctor McCoy from Rura Penthe in 2293.
   Named after the Illinois city.
   "Star Trek VI: The Undiscovered Country"
USS Strata NCC-
   Geo-terraforming vessel.
   "Field of Fire" - DS9.
USS Syracuse NCC-
   Shown as part of a personnel file (Alfonse D. Pacelli).
   "Eye of the Beholder" - TNG.
USS Ticonderoga NCC-
   Reported to the Ba'ku homeworld in 2375 to facilitate the planet becoming a Federation protectorate.
   Named to honor the capture of Fort Ticonderoga on May 10, 1775, by Ethan Allen and the Green Mountain Boys.
   "Star Trek: Insurrection"
USS Titan NCC-
   In 2378 Captain William Riker took command of this ship. His first mission was to head up a new task force for peace talks on
   Romulus.
   "Star Trek: Nemesis"
USS Tokyo NCC-
   One of 39 starships lost at the battle of Wolf 359.
   - TNG.
USS Tombaugh NCC-
   Assimilated by the Borg in 2360.
   "Infinite Regress" - VOY.
USS Trial NCC-
   Possibly a Miranda-class ship.
   "Way of the Warrior" - DS9.
USS Truman NCC-
   Not near DS9 in months according to Ezri Dax.
   "Field of Fire" - DS9.
USS Valiant NCC-1223
   Destroyed while contacting Eminiar VII in 2217 as a casualty of the 500 year war between Eminiar VII and Vendikar.
   "A Taste of Armageddon" - TOS.
USS Valiant NCC-75418
   Part of the fleet to rendezvous with the USS Enterprise NCC-1701-E to intercept the Reman warship Scimitar.
   It is possible this ship is also a Defiant-class named after the previous Valiant destroyed in the DS9 episode "Valiant".
   "Star Trek: Nemesis"
USS Vandor NCC-
   One of 39 starships lost at the battle of Wolf 359.
   - TNG.
USS Vega NCC-
   One of 39 starships lost at the battle of Wolf 359.
   - TNG.
USS Veracruz NCC-
   "The Siege of AR-558" - DS9.
USS Volga NCC-
   One of 39 starships lost at the battle of Wolf 359.
   - TNG.
USS Watley NCC-
   One of 39 starships lost at the battle of Wolf 359.
   - TNG.
USS Whorfin NCC-1024
   Potential participant in Operation Retrieve to rescue Captain Kirk and Dr. McCoy from Rura Penthe in 2293.
   "Star Trek VI: The Undiscovered Country"
USS Zetar NCC-
   One of 39 starships lost at the battle of Wolf 359.
   - TNG.
Name Unknown NCC-75227
   Starfleet scout ship used by Lieutenant Commander Data in 2375 in the Briar Patch.
   "Star Trek: Insurrection"
Name Unknown NCC-71325
   Registry to the shuttle that carried Paris and Lieutenant Stadi to Voyager while docked at DS9.
   The mothership to the shuttle was not seen, furthermore the shuttle registry changed to NCC-1701-D because of stock footage use.
   "Caretaker" - VOY.