Finnegan was the name of a flamboyant Irish upperclassman who tormented James T. Kirk during his time at Starfleet Academy. Looking back from the perspective of years, Kirk described himself as "positively grim" during that era, a fact that delighted jokester Finnegan immensely. The sort of fellow who would put a bowl of cold soup in your bed, or leave a bucket of water propped over a half-open door, Finnegan tormented Cadet Kirk mercilessly.
In 2267, the USS Enterprise discovered the Shore Leave Planet, a place where one's fantasies were made real. On that world, Kirk encountered a version of Finnegan, exactly as he had appeared so long ago. At that point, Kirk did not understand the nature of the planet, and so he sought answers from Finnegan, who was the first character that actually interacted with the landing party. These attempts earned Kirk only japes and mockery, and finally Kirk had enough – he chased down Finnegan and "beat the tar out of him" – something he'd been longing to do for years. During their fight, Finnegan offered a valuable clue in his statements, "Kinda makes up for things, huh Jim?" and, "I'm being exactly the way you remember me." At the end of the fight, Kirk and Spock realized that Finnegan, like all the other artifacts, had been created in response to Kirk's unvoiced desire for revenge. (TOS: "Shore Leave")
Finnegan was portrayed by actor Bruce Mars. At one point, Finnegan refers to Kirk as a plebe. Assuming this usage corresponds to modern naval usage, this would mean Kirk was a first year cadet at the time Finnegan tormented him, probably circa 2251 or so. There is a modern US Navy tradition of upperclassmen inflicting various sorts of odious duties on plebes at the United States Naval Academy, but Finnegan's antics seem to go beyond what is currently tolerated.
Finnegan is the only significant character to wear the early 23rd century Starfleet cadet uniform. Since Finnegan was a cadet in the 2250s, we can assume this uniform Kirk remembered him wearing was from that era. Since the costume was reused, unchanged, on Starfleet extras in late-2260s episodes, it establishes that cadets of both eras wore the same design of uniform. (TOS: "The Trouble with Tribbles", "Wolf in the Fold")
Finnegan appeared in the comic book stories "Starfleet Academy!" (Star Trek Annual (DC) volume 2 #2), "Old Loyalties" and "Finnegan's Wake!" (DC TOS volume 1 #54-55). The latter two stories depicted him in the 2280s, as a commander serving as an investigator in the Federation Security Legion who is sent to the Enterprise to investigate the attempted murder of Kirk. Although he takes the investigation seriously, Finnegan is still a prankster much to the frustration of "Jimmy" Kirk who fails in his own attempts to get even. Finnegan does acknowledge, in private, that Kirk has a genius for commanding crew loyalty.
A family member of Finnegan's made an appearance in the first of Peter David's Starfleet Academy books, remarking after playing a prank on Worf that he comes from a long line of Academy pranksters before Worf teaches him a lesson.