List of unnamed Federation starships of the J class.
Mudd's stolen starship
Harry Mudd's antiquated J-class vessel, in 2266.
A small class J cargo ship was in the possession of Harcourt Fenton Mudd in 2266. Although officially designated as a cargo ship, Mudd was using it as a transport.
On stardate 1329.1, Mudd was using this ship to transport three women to Ophiucus III to become wives for settlers on the planet when it was detected by the USS Enterprise. Being an unregistered, unidentified ship, Mudd's vessel was pursued by the Enterprise. In attempting to escape, Mudd burned out his ship's engines, leaving it powerless as it drifted into an asteroid belt. Although Mudd and his "cargo" of three women were rescued by the Enterprise, his J-class vessel was destroyed after impacting an asteroid.
According to Mudd, the former commander of this vessel was one Leo Francis Walsh. (TOS: "Mudd's Women")
Starfleet training vessel
In 2266, an old Class J starship was maintained by Starfleet for use as a cadet vessel for Academy trainees.
During a training mission aboard this vessel, one of the ship's baffle plates ruptured, exposing the engine room to delta radiation. Fleet Captain Christopher Pike suffered severe radiation exposure and eventual paralysis whilst attempting to rescue cadets trapped in the engine room. (TOS: "The Menagerie, Part I")