Eidetic memory, sometimes referred to as photographic memory or total recall, was a psychological term referring to an ability to recall images in near-photographic detail. People with such memory might claim to "see" spoken words. (Star Trek IV: The Voyage Home)
Federation doctors considered it an amazing gift. (VOY: "Eye of the Needle"). However, it was a normal trait in some species, including Borg and Cardassians. (VOY: "11:59"; DS9: "The Maquis, Part I")
In 2370, Gul Dukat noted that the controls on his side of a runabout he shared with Benjamin Sisko were not illuminated and therefore if an emergency arose, he could not pilot the runabout. When he assured Sisko that he was not interested in stealing the ship's technology, Sisko reminded him that he was well aware that Cardassians possessed photographic memories. Dukat then quipped, "So you turn off my controls so I don't have enough light to take my photograph, is that it?" (DS9: "The Maquis, Part I")
In 2371, upon quizzing Kes about anatomy which she had studied and finding all her answers to be correct, The Doctor voiced his suspicion that she had an eidetic memory and his intention to run a full neural scan on her later. (VOY: "Eye of the Needle")
In 2374, upon coming across an alien impostor in the guise of Tom Paris reading Captain Kathryn Janeway's personal logs, which "Paris" denied, Seven reminded "Paris" that she had an eidetic memory and needed only seconds to memorize what was written on the PADD. She asked if "he" would like her to quote from the log to prove it. (VOY: "Vis à Vis")
In 2375, Luther Sloan praised Julian Bashir's ability to remember facts about various Romulans, saying that total recall was a good ability for an operative to possess. (DS9: "Inter Arma Enim Silent Leges")
Also that year, after Seven of Nine correctly named the seventh wonder of the ancient world, the Lighthouse of Alexandria, its builder and the year, Tom Paris remarked, "Behold the wonder of the modern world. Borg photographic memory." (VOY: "11:59")
Being an android, Data's memory record had eidetic functionality. Furthermore, in "The Cloud" it was stated that Harry Kim had memory of his being in his mother's womb.