In 2266, Harcourt Fenton Mudd possessed an unregistered small class J cargo ship which he utilized as a transport vessel. While attempting to outrun the Enterprise, Mudd piloted the ship into an asteroid belt, in the process causing his engines to overheat. Disabled, the ship was ultimately destroyed by an asteroid collision, but not before the Enterprise was able to beam off all of the ship's inhabitants. (TOS: "Mudd's Women")
The same year, Starfleet maintained an old class J starship for use as a cadet training vessel. During an inspection by Fleet Captain Pike, a baffle plate ruptured, exposing the crew to harmful delta rays. Pike received an extremely high dose which ultimately left him an invalid, as he went in to rescue the cadets. (TOS: "The Menagerie, Part I")
The Deneva colony also had a class J starship at their disposal, described as a one-man vessel of Denevan configuration. The USS Enterprise was unable to intercept it, after it came into sensor range, even at warp 8 before it was destroyed by the heat of the Denevan sun. (TOS: "Operation -- Annihilate!")
In 2269, the Federation operated the space cruiser Aurora. The ship was stolen by Dr. Sevrin and five of his followers in search for the mythical planet Eden. The ship was destroyed when attempting to pull free from a tractor beam. (TOS: "The Way to Eden")
Ships of the class
It was initially believed that when the J class was introduced in Star Trek: Enterprise that the writers were tipping their hat to the ship class that was twice referenced in the original Star Trek. This association was discovered to be false when "Mudd's Women" was remastered and Mudd's ship was given a completely new design from what was shown in Enterprise.
Slight variations were made in this design's three remastered appearances. In the case of the Denevan starship, the original class J model, albeit slightly scaled down, was a reused to represent that ship as well. In the case of Aurora the engines were slightly modified and new windows were added.
The remastered design shares a similar design lineage to a number of early Matt Jefferies' "shuttlecraft/scout craft" sketches featured in the Star Trek: The Original Series Sketchbook (pg. 86-87). Jefferies' "curved shape" designs were ultimately rejected for being "too expensive", in favor of the design that would be associated with the Class F shuttlecraft.