Throughout its long and storied franchise history, Star Trek has boasted a number of iconic and powerful spaceships. In fact, most of the shows in the franchise are named after the ships that the characters are traveling on through their adventures in space, like Voyager, Enterprise and Discovery. The vast majority of Star Trek ships travel via warp drive, but despite being able to travel at such a fast speed, there is a limit to how fast warp can take a starship of any fleet.
The warp factor of an average Starfleet vessel usually ranged from "Warp 1" to "Warp 10," with 10 being a nearly impossible speed to achieve under normal circumstances. Many crews, including that of the Enterprise-D and the stranded USS Voyager, have tried to break through this pesky speed ceiling. Though most ships in Starfleet operate at well below Warp 10, one Starfleet vessel has made it close enough to the limit without major repercussions to the ship's integrity: the USS Prometheus.
The Prometheus first appeared in the Voyager episode "Message in a Bottle." In the episode, The Doctor is sent over to the Prometheus, which has been stolen from Starfleet by Romulans. He learns that the experimental prototype ship has regenerative shielding, ablative hull armor, and a mulitvector assault mode. The Doctor also learns that the ship can travel at Warp 9.9, which is faster than any other Starfleet craft. Despite its brief appearance, the Prometheus actually plays a huge role in the series, as The Doctor is able to use the ship to contact Starfleet Command and inform them of Voyager's status in the Delta Quadrant.
The ability to travel at nearly Warp 10 makes the Prometheus the fastest ship in Starfleet, and possibly the galaxy. Other ships have come close to the Prometheus in terms of speed – contemporary vessels such as the Enterprise D and E, as well as Voyager and Defiant (and even Borg Cubes), could all go above Warp 9 at top speeds. Technically, the U.S.S. Discovery can travel instantaneously across space via the mycelial network, but in terms of warp factor, the Prometheus is the fastest ship in the fleet.
The incredible speeds that the Prometheus can fly also doesn't seem to cause any major malfunctions or side-effects associated with the high warp factor. But, going that fast usually stresses a ship's capabilities, which is why most ships travel at a much slower warp factor. Star Trek has often explored what would happen if a ship crosses warp factor 10. Usually, a crew's attempts to cross the barrier has almost always resulted in some sort of catastrophe, such as in the notorious Voyager episode "Threshold."
There is a chance that Starfleet may be able to pass Warp 10 at some future date. Thanks to a possible future depicted in the series finale of Star Trek: The Next Generation, ships might be able to travel at speeds like Warp 13. But for now, the USS Prometheus holds the title for fastest Starfleet ship.