(covers information from several alternate timelines)
The following is a list of unnamed Federation starships in service during the 24th century.
Contents
By assignment
Bergan's mother's ship
This starship was scheduled for a rendezvous with the USS Melbourne at Wolf 359. The ship received a warning from Starfleet about the Borg attacking the sector; however, the message was received too late for the ship to turn around. During the Battle of Wolf 359, the ship was severly damaged, with individuals escaping in escape pods. At least one of these individuals, the mother of Melbourne officer Gregory Bergan was assimilated by the Borg. (VOY: "Infinite Regress")
Chakotay's first assignment
This starship was the first assignment of Chakotay's out of the Academy. During his tenure aboard, the ship was assigned to make first contact with the Tarkannans. Chakotay envied the role so much that he pestered the Captain into letting him be part of the diplomatic team. (VOY: "Innocence")
Diego's starship
This starship was commanded by Captain Diego in 2374.
In that year, the ship participated in Operation Return. (DS9: "Sacrifice of Angels")
Kim's deep space assignment
In an alternate timeline, this deep space vessel was assigned to exploration in the region of space directed toward the Delta Quadrant.
Following Chakotay and Harry Kim's successfully returned to Earth in 2375, aboard the Delta Flyer, and at the cost of the loss of USS Voyager, Kim experienced incredible survivor guilt. He signed onto this, the first deep space vessel he could find, in order to locate Voyager. According to Kim, "We tried to calculate where Voyager might have fallen out of the slipstream." They searched for four years, and according to Kim, "We were close, I could feel it!", but Starfleet Command had other ideas, and called off the search in 2381, citing a "low probability of success," forcing Kim to ultimately resign Starfleet and pursue his own search. (VOY: "Timeless")
Hayes' starship
Admiral Hayes commanded a starship sometime before the Battle of Sector 001 in 2373. During the battle, this ship commanded the Federation fleet until its destruction. (Star Trek: First Contact)
Picard's starship
This starship was commanded by Captain Jean-Luc Picard in the 2360s. His ship responded to a distress call from colonists in the Carnelian minefield. (TNG: "Legacy")
Ross' flagship

Ross on his flagship
This starship utilized by Admiral Ross during the Dominion War.
In early 2375 he travelled to Deep Space 9 aboard this ship when he wished to speak to Colonel Kira Nerys in person about the Romulans establishing a permanent presence on that station. (DS9: "Image in the Sand")
Later that year, this ship served as his flagship as he led the Federation part of the allied fleet in the Battle of Cardassia from this ship. (DS9: "What You Leave Behind")
Sisko's transport
This starship took Benjamin Sisko and his son Jake to Deep Space 9 in 2369 while commanded by a captain. The starship featured a holodeck and an observation window where the pair viewed Deep Space 9 for the first time. (DS9: "Emissary")
Troi's transport vessel

Troi's transport ship
This small transport vessel was used to ferry Ambassador Lwaxana Troi to the USS Enterprise-D in 2365.
Yar's early assignment
This starship was Natasha Yar's assignment before her transfer to the USS Enterprise-D in 2364. The ship responded to a distress call from colonists in the Carnelian minefield. The ship's captain owed a favor to Jean-Luc Picard. (TNG: "Legacy")
By mission
Angel I visit
This vessel visited the planet Angel I in 2302. (TNG: "Angel One")
Battle of Sector 001 combatant

Cylindrical ship at the Battle of Sector 001
This ship fought against the Borg in the Battle of Sector 001 in 2373. (Star Trek: First Contact)
Epsilon IX starships

Portion of Rocha's log mentioning these ships
According to Keith Rocha's personal logs, at least half a dozen starships were in the vicinity of Epsilon IX station. He speculated that it might be due to some big science project. (TNG: "Aquiel")
Klavdia III charter mission
In 2349, this ship took Salia and Anya, following the death of Salia's parents, from their homeworld of Daled IV to Klavdia III so that Salia could be raised in a neutral environment.
It was the mission of the USS Enterprise-D to return the two back to Daled IV, from Klavdia III, in 2365. (TNG: "The Dauphin")
Qualor II starships
These two starships were among the collection at the Qualor II Surplus Depot D15 in 2367. (TNG: "Unification I", "Unification II")
Search vessel
When the mining shuttle Nenebek disappeared in the Pentarus system, the USS Enterprise-D contacted the nearest unnamed starbase. The starbase sent a message back saying the closest search vessel was almost a week away. (TNG: "Final Mission")
Closest help
In 2367, after the loss of the USS Lalo to a Borg cube, Starfleet Command contacted all the available starships near the last position of the Lalo to assist the USS Enterprise-D in a possible confrontation with the Borg. This starship, the closest to help, was six days away. (TNG: "The Best of Both Worlds")
Sector 2158 starships
In 2370, these two starships were sent to the planets Yadalla Prime and Draken IV in Sector 2158, with the stated intention of intercepting a mercenary vessel before it could attack those planets. (TNG: "Gambit, Part II")
Starbase 74 ships
These two starships were docked, along with the USS Melbourne, at Starbase 74 when the Bynars commandeered the USS Enterprise-D. (TNG: "11001001")
Tau Cygna V evacuation ship
The evacuation ship was a colony transport ship equipped with dedicated personnel shuttles. It was sent by Starfleet to Tau Cygna V, where it would assist in the evacuation of the Human colony from that planet in 2366. (TNG: "The Ensigns of Command")
Torona IV diplomatic mission
This starship visited Torona IV in 2344 with a mission of opening diplomatic talks with the Jarada. The ship's captain failed in his pronunciation of the greeting thus ending diplomatic talks between the Jarada and the Federation for twenty years. The record tapes of this encounter were viewed by the USS Enterprise-D crew in 2364 as they prepared for their attempt in opening diplomatic relations with the Jarada. (TNG: "The Big Goodbye")
By type
Deep space vessels
In 2377, two deep space vessels were redirected toward the position of USS Voyager. A rendezvous of the three ships was expected sometime in 2382 or 2383. Admiral Hayes mentioned these ships in a message sent to the Voyager. (VOY: "Life Line")
Science vessels
In 2369, Starfleet dispatched two science vessels to study a newly-discovered Dyson sphere. (TNG: "Relics")
Starfleet Medical courier
A Starfleet Medical courier was to rendezvous with the USS Enterprise-D at Star Station India in 2365. Starfleet Command viewed this mission as very important. (TNG: "Unnatural Selection")
Starfleet transport
In early 2375, a Starfleet transport carrying mainly Vulcan wounded requested permission to dock at a Romulan hospital on Derna, but was turned away. (DS9: "Image in the Sand")
Supply ship
In 2367, Paul Hickman's stolen Type 7 shuttlecraft, on a course toward Tarchannen III, was spotted by a supply ship roughly 24 hours before stardate 44664.5. (TNG: "Identity Crisis")
Survey ship
In 2369, this survey ship and a Vulcan science vessel were the only two ships that had departed Deep Space 9 on the day that Ibudan was murdered. (DS9: "A Man Alone")
Vulcan transport
This transport had a scheduled run from Vulcan to Deep Space 9 in 2371.
On this particular trip, it was supposed to be carrying medical supplies on behalf of Doctor Julian Bashir, but became delayed. This delay forced Bashir the possibility of himself being behind schedule for the colonization effort he was due to take part in, using said supplies. (DS9: "Defiant")