This page contains information regarding Star Trek: Lower Decks, and thus may contain spoilers.
In December of 2000, a football game was being shown on a television at a bar in Portage Creek at which Shannon O'Donnel and Henry Janeway found themselves. One team participating in that game was Baylor. (VOY: "11:59")
In 2024, Biddle "B.C." Coleridge complimented Benjamin Sisko (who had assumed the identity of Gabriel Bell) on his tackle and asked whether he had ever played football, to which Sisko replied, "Baseball, actually." (DS9: "Past Tense, Part II")
Aboard the Earth Cargo Service freighter ECS Fortunate in 2151, Captain Keene and his first officer, Matthew Ryan, repeatedly passed a football back and forth to each other with the gravity plating turned off between them, allowing the ball to float freely from one catwalk to the other in cargo module 4. Keene quipped that Ryan would not be able to catch the ball if the grav-plating was set at Earth sea level. Ryan retorted that Keene would not be able to throw the ball ten meters on Earth. (ENT: "Fortunate Son")
A Vulcan anthropologist once witnessed a football game, and incorrectly reported that the aim of the game was for the players to attempt to "kill the quarterback." Kov had heard this report, and in 2151 asked Commander Tucker about the details, which he straightened out. (ENT: "Fusion")
In 2375, Kasidy Yates asked Ryan, a guard in Vic's Las Vegas Lounge, if he had been the captain of the football team at a high school in Asheville, North Carolina. He admitted that he had "played a little football" in high school. (DS9: "Badda-Bing, Badda-Bang")
In 2380, Q set a challenge for the bridge crew of the USS Cerritos by placing them on a giant chess board with elements of several different sports and games. One of those elements was goal posts from football, placed at either end of the board. (LD: "Veritas")