(covers information from several alternate timelines)
This page contains information regarding Star Trek: Discovery, and thus may contain spoilers.
First Contact Day was a holiday celebrated to honor both the warp 1 flight of the Phoenix and first open contact between Humans and Vulcans on April 5th, 2063 in Bozeman, Montana. (Star Trek: First Contact)
The mirror universe equivalent of First Contact Day was also on April 5th. Instead of peacefully greeting the Vulcans, the Terrans slaughtered all of the members of the survey ship. The day was later celebrated as a holy day by the Terran Empire. (ENT: "In a Mirror, Darkly"; DIS: "Die Trying")
When Captain Kathryn Janeway was a child, the holiday was just considered a day off from school. Later, at least some schools such as WSA continued to operate on First Contact Day. (VOY: "Homestead"; ST: "Children of Mars")
Naomi Wildman and Neelix planned the 315th observation of the event aboard the USS Voyager. The festivities included Zefram Cochrane's favorite food, cheese pierogies, and rock and roll music on Tom Paris's jukebox. At Neelix's insistence, Tuvok gave the Vulcan salute while reciting the greeting given by the Vulcans during first contact: "Live long and prosper." He did not see the point of it, but everyone in attendance applauded. (VOY: "Homestead")