The forty first academy marathon, over a distance of forty kilometers, was held in April of 2323 on the planet Danula II. Jean-Luc Picard passed four upper classmen on the last hill, becoming the first, and as of 2367 the only, freshman cadet to win the marathon. A considerable amount of training preceded it. (TNG: "The Best of Both Worlds, Part II", "Chain of Command, Part I"; Star Trek Nemesis)
Admiral J.P. Hanson described this as "the damndest thing I ever saw", and decided to make getting to know Picard his business, a sentiment he recalled after Picard was converted into Locutus of Borg in 2366. Picard kept a certificate pertaining to the win in the Picard family album. (Star Trek Nemesis)
Background information Edit
Along with the rest of the family album, this certificate was initially created for Star Trek Generations, though it was not seen in that movie. A behind-the-scenes feature in the July 2002 issue of Star Trek: The Magazine (Volume 3, Issue 03, Page 70) offered the better view depicted here.
The distance, forty kilometers is slightly shorter than the modern marathon by approximately two kilometers, or just over one mile.
According to his dossier on the official Star Trek site, in the alternate reality Pavel Chekov won the Academy marathon some time before his mission on the USS Enterprise in 2258, and was the youngest cadet to do so at the time.  The Gemini Agent depicts him training for the event by running barefoot, and reveals that the previous record holder was 18 at the time.