According to the Bible, the central text of the Earth religions Christianity and Judaism, Adam and Eve were the first Humans on Earth that were created in the image of God. They were later cast from the Garden of Eden after succumbing to temptation of the Devil and disobeying God's law. (TOS: "The Apple")
In 2254, when Christopher Pike was abducted by the Talosians, he was placed in a position to begin a new population of Humans on Talos IV, where he was allowed to choose his mate. His options were limited to Vina, "Number One" and J.M. Colt. After their subsequent release, Colt later inquired of Pike as to who his choice for "Eve" would have been – a question Pike found inappropriate. Intrigued, Dr. Boyce inquired, "Eve as in Adam?", to which Pike replied, "As in all ships' doctors are dirty old men." (TOS: "The Cage")
In 2268, Sargon speculated that the story of Adam and Eve had been inspired by two travelers of his species which explored the galaxy 600,000 years prior. (TOS: "Return to Tomorrow")
In 2269, Spock commented on the irony that, like his Biblical namesake, Adam had been punished for eating fruit from "Eden". (TOS: "The Way to Eden")
Spock kept an image of the 20th century art piece Adam and Eve Expelled from Paradise in his quarters aboard the USS Enterprise-A during the late 23rd century. The expulsion of Adam and Eve from paradise, was to him, a representation that reminded him that all things must end. (Star Trek VI: The Undiscovered Country)
Brenna Odell, upon hearing that the Bringloidi were being resettled on the planet Mariposa under the condition of having three children with three different men to revive the gene pool at the Mariposa colony, was unsure if she wanted to be "Eve." (TNG: "Up The Long Ladder")
When trying to explain how a CHAH-mooz-ee ended up on an uninhabited moon in the Delta Quadrant, Chakotay referenced a legend of the Sky Spirits. He put no more faith in these myths than Janeway did in Adam and Eve as an explanation for the origin of life on Earth. (VOY: "Tattoo")