(covers information from several alternate timelines)
A .45 automatic was a series of semi automatic pistols made by Colt Firearms used during the 20th century on the planet Earth.
Characters in the Dixon Hill series of novels, set in the early 20th century, often carried them. (TNG: "The Big Goodbye")
The United States military used this projectile weapon during and after World War II. In an alternate 1944, resistance forces fighting the Wehrmacht in the United States were armed with these weapons. (DS9: "Little Green Men"; VOY: "The Killing Game", "The Killing Game, Part II"; ENT: "Storm Front", "Storm Front, Part II")
US Marine sentries used a .45 automatic variant on board the aircraft carrier USS Enterprise and aimed them at Pavel Chekov during his arrest in 1986. (Star Trek IV: The Voyage Home)
In the Hotel Royale simulation, Mickey D, the owner of the Hotel Royale, owned a nickel-plated .45 automatic. He fired this weapon at the bellboy over a dispute about who had rights to Rita, killing the young man. (TNG: "The Royale")
By 2268, the inhabitants of the planet Sigma Iotia II had developed their own copy of the .45 automatic, along with other 1920's-era Earth firearms, when they based their culture off descriptions of that era's Chicago gangs. (TOS: "A Piece of the Action")
In 2375, Chief O'Brien commented that due to the jack-in-the-box planted in the Bashir 62 holoprogram by Felix, the character Frankie Eyes would need to be killed by a period specific weapon like a .45 automatic and not a phaser. (DS9: "Badda-Bing, Badda-Bang")