Kidnapping or abduction was the act of an individual or individuals being forcibly taken without their consent.
In 2153, Admiral Maxwell Forrest expressed his thoughts that the A-6 excavation team was abducted by a technological advanced species. (ENT: "Regeneration")
A year later in 2154, Klingon Augments kidnapped Phlox and used him in their experiments to make more. Archer in his crew rescued Phlox and distributed the cure but it would take 50 earth years until the Klingons returned to normal. (ENT: "Affliction" "Divergence")
In 2270, James T. Kirk told Montgomery Scott that he believed the USS Enterprise's computer had kidnapped three crew members. (TAS: "The Practical Joker")
In 2364, after several children were kidnapped from the USS Enterprise-D, including Wesley Crusher, Rashella attempted to acclimate him to life on Aldea. She instructed Wesley on the use of the Custodian and attempted to answer his questions concerning their world. (TNG: "When The Bough Breaks")
After being rescued in 2366, Data asked William T. Riker to arrange to take Kivas Fajo into custody for murder, kidnapping and theft. (TNG: "The Most Toys")
Q kidnapped Jean-Luc Picard in 2365, sending him into a shuttlecraft far away from the USS Enterprise-D. (TNG: "Q Who")
In 2366, DaiMon Tog kidnapped Lwaxana Troi as well as Starfleet officers Deanna Troi and William T. Riker. (TNG: "Ménage à Troi")
That same year on Stardate 43714.1, a group of aliens kidnapped Captain Picard and replaced him with an imposter who steered the Enterprise into a pulsar. Captain Picard was able to foil his captor's plans and was returned to the Enterprise where the imposter was unmasked. (TNG: "Allegiance")
That same year on Stardate 43989.1 Captain Picard was kidnapped by the Borg and forced to lead an attack on the Federation Fleet at Wolf 359. Data and Worf used a shuttle to get him back and returned him to Enterprise where his implants were removed. (TNG: "The Best of Both Worlds", "The Best of Both Worlds, Part II")
The Caretaker abducted people for several months, probed them, and sent some to the city of the Ocampa beneath the surface of their planet. Harry Kim and B'Elanna Torres became the last people abducted by the Caretaker. (VOY: "Caretaker")
The Doctor was kidnapped by Gar in 2377 and sold to Chellick to treat patients on the Dinaali Hospital Ship 4-2. (VOY: "Critical Care")
On Quarra, Criminal Investigations was the department in charge of investigating abductions. (VOY: "Workforce, Part II")
In 2381, Nick Locarno kidnapped Beckett Mariner with the intent of recruiting her into Nova Fleet. When Mariner asked if she was a prisoner on Nova One, Locarno insisted he had rescued her from the Klingons and Romulans stranded on Sherbal V, but she protested that she had not needed saving. Not noticing her increasingly stark discomfort with what he was doing, Locarno attempted to use Mariner to recruit lower deckers to join Nova Fleet, but she instead denounced him on a live broadcast and fled, leading to a chase around the Detrion system that lasted until she was rescued by the USS Cerritos. (LD: "The Inner Fight", "Old Friends, New Planets")