A suicide mission or suicide plan was a mission considered to be so dangerous or brash for the participants involved that its undertaking would be certain suicide.
Captain Archer volunteered for a suicide mission to destroy the Xindi weapon. However, he failed and was captured by the Xindi-Reptilians. (ENT: "Azati Prime")
In the mirror universe, in order to give time for the rest of his crew to reach escape pods, Maximilian Forrest stayed aboard the ISS Enterprise as it was being destroyed by the Tholians. (ENT: "In a Mirror, Darkly")
In the alternate reality, following a devastating attack on the USS Kelvin by the Narada, acting captain George Kirk was forced to stay on board the Kelvin and set a collision course with the Narada after the auto pilot controls were destroyed. His actions helped save the fleeing shuttlecraft, which had abandoned ship on Kirk's orders. (Star Trek)
In 2259 of the alternate reality, Captain James T. Kirk had entered the reactor core to restore power to the disabled USS Enterprise that was plummeting towards Earth knowing full-well he would be poisoned from the radiation. (Star Trek Into Darkness)
In 2268, Doctor Leonard McCoy volunteered to take a shuttlecraft for a closer look at the space amoeba to pinpoint its vulnerable spots but Captain James T. Kirk considered it a suicide mission. (TOS: "The Immunity Syndrome")
As the USS Enterprise approached the galactic barrier after being hijacked by the Kelvans in 2269, Captain James T. Kirk had Spock and Montgomery Scott devise a suicide plan to stop them by rigging the ship to explode on Kirk's command. (TOS: "By Any Other Name")
In order to repair the warp engines of the Enterprise, Spock entered a radiation-flooded reactor room well knowing that he would probably not survive. (Star Trek II: The Wrath of Khan)
In 2368, Q, stripped of his powers and the cause of the Calamarain attacks on the USS Enterprise-D, left the ship in a shuttlecraft in an attempt to sacrifice himself and save the ship. (TNG: "Deja Q")
In 2368, in order to reach main engineering of the Enterprise and repair the antimatter containment field, Data had to take a chance of being electrocuted and killed. (TNG: "Disaster")
In 2372, Kathryn Janeway and Tuvok stayed on board the USS Voyager while the ship's self-destruct sequence was active. (VOY: "Dreadnought")
In an alternate 2374, Janeway made a suicide run at the Krenim weapon ship. (VOY: "Year of Hell, Part II")
In 2375, B'Elanna Torres performed a number of holodeck simulations in which the safety protocols had been deactivated. In one simulation involving a recreation of the Delta Flyer, she was knocked unconscious as the vessel entered the atmosphere, and may have died had it not been for a vigilant Chakotay. (VOY: "Extreme Risk")
Also that same year Gowron attempted to send Martok on a suicide mission to Sarpedion V. Benjamin Sisko and Martok refused the plan as too risky and Martok and Worf challenged Gowron to a duel which Worf won and Worf crowned Martok Chancellor of the Klingon High Council. (DS9: "Tacking Into the Wind")
In 2379, Captain Jean-Luc Picard beamed aboard the Reman warbird Scimitar in an attempt to destroy the thalaron generator, which was only minutes from activating. The USS Enterprise-E transporters went down shortly after he was beamed aboard the Scimitar, so a rescue would have been impossible. (Star Trek Nemesis)
Commander Data sacrificed himself to destroy the Scimitar by firing a hand phaser at the thalaron generator, knowing he would not survive the resulting explosion. (Star Trek Nemesis)