The United Federation of Planets is a federal republic with a universal reach in the Star Trek universe. Starfleet is the wing of the Federation that covers exploration, scientific research, peacekeeping, and defense. Naturally, they would have to have an impressive fleet to maintain their interstellar reach. The following ships are the fastest that Starfleet has to offer. Some of these ships were designed and intended for speed or travel while others were modified later for specific missions.
10 USS Monitor, Nebula Class
Often used as a scouting ship or for important deliveries because if it's maneuverability and speed, this ship is the proverbial Hermes of Starfleet. If there's a word about a ship that's been lost or destroyed or the Romulans are about to attack, send in the USS Monitor. The ship appears in several episodes of TNG television series and the Star Trek Generations video game doing exactly this. She does appear in combat but her real strength is in movement. The whole Nebula-class was designed with science and exploration in mind as opposed to offensive trips. Each is equipped with warp nacells on both the primary and secondary hull.
9 USS Ajax, Apollo Class
The crew of Star Trek, The Next Generation (TNG) were not only exploring the universe but also the limits of technology. Kosinski was a propulsion expert who was a recurring character on TNG, and the USS Ajax was one of the first ships that got his experimental transwarp drive upgrades. Starfleet command views it as a faster, more maneuverable ship since she's seen equal amounts of battle, exploration and travel time. In the original TNG episodes, she's described as part of the Excelsior class but this detail was retconned and she was officially listed in the internal Starfleet records as an Apollo-class vessel.
8 USS Discovery, Crossfield Class
The main setting for Star Trek: Discovery, the whole motive for this ship's existence is to research and measure speed. The entire Crossfield class was designed to test an experimental spore drive and other potential sources of propulsion that exceed the speed of light.
As much of this story takes place in the early days of Starfleet, some of the missions and experiments of the USS Discovery are very secretive or surrounded by tight security. After the ship was presumably destroyed after being consumed by a wormhole, her secrets would list in deep space for a thousand years. Any survivors that knew about the secret experiments, including the spore drive, were compelled to remain silent or be charged with treason
7 USS Fearless, Excelsior Class
A descendant of the original Excelsior, this is another ship from TNG era. In addition to the original design of the class that emphasized speed, the USS Fearless was also an early recipient of Kosinski's experimental upgrades. She combines both the power of the transwarp drive that the Excelsior class is known for along with the brilliant inventions of Kosinski. In the TNG episode in which she appears, the Enterprise-D gets the same upgrades. Mapping and exploration was her specialty, and in the TNG episodes where the Fearless is mentioned, she's always making maps or exploring another new galaxy.
6 USS Enterprise, Sovereign Class
Also known as the Enterprise-E, this model was designed in part by Montogomery Scott himself, so you know it has all the best of the models from the original right up until the Enterprise-D. Officially it can reach a speed of Warp 9.9 thanks to cutting-edge design and minor but effective fixes, like moving the warp nacells upwards and forward.
This is the ship that you see in the Star Trek movies that feature The Next Generation cast. It also makes an appearance in the Star Trek: Bridge Commander video game.
5 USS Voyager, Intrepid Class
It goes far and fast, thanks to its original design and several modifications during her years of wandering the unknown reaches of space. This ship was the first to cover the whole Delta Quadrant, a notable feat even if it was during an improvised seven-year mission. These Intrepid class ships were built for tough, long exploration assignments. Among several other modern features, they were the first Starfleet ships to have Warp 9 class drives, specifically tweaked for use in deep space. During their journey, the ship improved even more, not only for better speed and defense but just to get home.
4 USS Excelsior, Excelsior Class
You can argue that a ship is only as good as her captain. That would explain the Excelsior's rather embarrassing debut in Star Trek III: The Search for Spock and the heroic exploits that set her apart in Star Trek VI: The Undiscovered Country. In the earlier movie, the Excelsior was sent to intercept the stolen Enterprise. Thanks to some neat sabotage on the part of Scotti, she didn't get very far. Under the capable hand of Captain Hikari Sulu a few movies later, however, the gutsy former helmsmen threatened to "fly her apart" instead of slow her down when rushing to the aid of the wayward Enterprise. One of the first ships fitted with transwarp drive, she was the prototype of what would become a whole class of fast ships.
3 USS Vengeance, Dreadnought Class
As if the less than optimistic name doesn't give it away, this ship is unique to any other in the Star Trek universe in many other ways. She lacks any serial number or distinguishing markings and operates in secret, carrying out clandestine and often extremely unethical missions with a military focus. This ship only exists in what is called the Kelvin Timeline, the alternate universe that was created with the Star Trek reboot in 2009.
The only ship of her class, the USS Vengeance was not only capable of great speeds but she can actually catch up to and attack a ship mid-warp. The crew is saved in this case by Scotti, who is sabotaging the fearsome warship from within. Does that sound familiar?
2 USS Prometheus, Prometheus Class
This ship includes Starfleet's most cutting edge technology when it comes to defense, offense, and speed. It's still mostly an experimental ship and continues to be under development, but word travels fast and the Romulans have already tried to steal her secrets. The day she was launched she was the fastest ship in the entire fleet and was designed to reach speeds of Warp 9.99. It might have been the improved technology that allowed the USS Voyager to contact Starfleet from the remote Delta Quadrant, ending seven years of isolation for another ship known for its speed.
1 USS Enterprise, Constitution Class
There are several ships in Starfleet that carry the famous Enterprise moniker, so just to clarify this is NCC-1701, the original ship that was destroyed at the end of Star Trek III, The Search for Spock. In Star Trek TOS, the maximum speed of the ship was officially Warp 8, but in the TOS Episode 3x14, That Which Survives, the ship reached a speed of Warp 14. Granted, this was due to damage that made impossible to slow the ship down, but the ship was still able to maintain that velocity. Although she wasn't designed specifically to be fast, both a warp drive and an impulse drive made her capable of long-term exploration and quick maneuvering. There was also the dedicated genius of Montgomery Scott that kept the Enterprise running in top form.