Phlebotinum Girl/Sandbox

""Men are perhaps born to fight each other. And women are perhaps fated to be their tools.""

- Reccoa Londe, Mobile Suit Zeta Gundam

Phlebotinum Girl refers to a series of Expies popular in Science Fiction Anime and Manga, that became popular enough to develop into their own Archetype. This trope may have been popularized and codified by Lala Sune from the anime Mobile Suit Gundam, though it's difficult to say for sure where it originated, as it is now so common.

To qualify as a Phlebotium Girl, a character must meet the following:
 * The character is a female lead and often a Love Interest to The Hero in a Science Fiction or occasionally Fantasy work, and is teenaged or in her twenties with an other-wordly appearance.
 * The character has a special ability (often border-line magical) or talent which is extremely desirable in the setting and usually one-of-a-kind or incredibly rare. Often she pilots the latest Super Prototype Mecha or is otherwise the key to some kind of power. If the "Phlebotinum" part of the girl is a born trait, and there are many other Phlebotinum Girls in the universe, then she may be part of a Bizarre Baby Boom or a set of Designer Babies, but she will still be the main focus and often "super special", either because of the unusual amount of power she possesses or by being one of the first to have this power.
 * The character is thrust into conflict and battle, often against her will and may be a Living MacGuffin, with many factions vying to possess her.

Other common but not universal traits include:
 * The character isn't a normal human, but is a Human Alien or Rediculously Human Robot, is an advanced human or mutant, or a specially created being. I Just Want to Be Normal is a very common desire of hers.
 * The character is physically or mentally frail, passing out often or getting sick, usually from her ability, or is just going crazy or depressed.
 * The character is a tragic figure, sometimes oppressed or manipulated by a Mad Scientist or other crazy person, and usually has little freedom of her own, instead following the orders of whatever person or organization controls her, sometimes blindly or without the will or courage to rebel. Even if she is owned by the 'good' side, she will often be forced to do things she doesn't want to, such as participate in battle and even kill people.
 * The character is prone to having a mental breakdown or HBSOD of some kind in her series at least once, perhaps as a response to some horrible thing she has been forced to do, the Phlebotinum she controls effecting her mind and taking control of her, or her controllers using some method of mind-control on her. Sometimes The Power of Love can break her mind control or otherwise leads to her freedom.
 * The character is the pilot of a Super Prototype Mecha OR The Hero is the pilot and she is the key to making it work, often involving some kind of advanced interface with the neural system. She also tends to
 * The character meets her end, being much more likely to die at the end of the series than your average lead.

The Phlebotinum Girl is extremely likely to cross-over with the tropes MacGuffin Girl, Barrier Maiden, Apocalypse Maiden, Living Battery, Mysterious Waif and Girl in a Box.

The Rei Clone is a very similar phenomena, Rei herself initially being one of these. Also compare Spaceship Girl and MacGuffin Girl.

Anime/Manga

 * The Gundam franchise has had a number of these, across different series:
 * Mobile Suit Gundam -- The Trope Codifier. Lalah Sune may represent an unbuilt version of this trope, as she was fiercely loyal to her CO and her romance arc did not end very well
 * Both Psyco Gundams were piloted by four women between them
 * Mobile Suit Gundam: Char's Counterattack -- Quess Paraya, like Lalah Sune, meets a tragic end before The Power of Love can accomplish anything
 * Mobile Fighter G Gundam -- The Devil Gundam's final host was Rain.
 * Mobile Suit Gundam The 08th MS Team -- Aina starts out as a subject of experiments in Zeon, but by the end, she has eloped with the hero.
 * Mobile Suit Gundam Wing -- Heero Yui is a male example, able to use the Zero system and fighting because others tell him to. He is slowly persuaded to the side of pacifism by Relena Peacecraft.
 * Mobile Suit Gundam SEED Destiny -- Stellar Loussier. She's raised from birth to not know anything except to kill or pilot a Gundam, gets memory cleanup and drugs every now and then. The word "die" or "death" is a safety feature they devised to control her just in case. It backfires sometimes...
 * Mobile Suit Gundam 00 -- Soma is one of only two surviving products of a Super Soldier project and ends up fighting against Celestial Being. Subverted in that her CO is a good guy who considers her to be like his own daughter.
 * Armored Trooper VOTOMS -- Fyana is a Super Soldier who ends up with the hero, Chirico, fairly quickly. Her old handlers try to get her back.
 * Basquash -- Rouge is an interesting case because she starts as the hero's love interest. It is only later that she gets drugged-up to become a powerful Basquash player.
 * Claymore -- Claire in particular is this for Raki, pre-timeskip.
 * Eureka Seven -- Eureka was this in her backstory, the key to piloting the Nirvash, and was rescued by Holland. Anemone is this in the present  and is rescued by Dominic.
 * Iriya no Sora UFO no Natsu -- has Kana Iriya piloting a super-advanced fighter jet. She's not oppressed, but she is the only one who can pilot it.
 * Macross II -- Ishtar is an emulator, a tool of the Marduk who can motivate Zentran to fight to the death with creepy singing. She is rescued by the hero early on, so naturally the Marduk try to recapture her.
 * Neon Genesis Evangelion -- Both Shinji and Rei are this.
 * Super Dimension Fortress Macross -- Lynn Minmei is an interesting case as she has no unnatural abilities whatsoever, and she is on the good guys' side.
 * El Cazador de la Bruja -- Ellis.
 * The dicloni of Elfen Lied -- natural born Tyke Bombs for bonus points.
 * Lachesis subverts this -- she's s remarkably stable and positive individual to the point of being a Genki Girl, is Happily Married to a man she loved since her childhood, and despite going through a lot she never lost her cool. But she's definitely an exception.
 * Melfina is this for the Outlaw Star. Both she and the ship were created to locate a legendary space treasure built by an ancient alien race.

Video Game

 * Blaz Blue has Noel Vermillion (who was really Mu-12 all along) after she's mindraped and "tempered" into a Living Weapon by Terumi, ) and Ada, Carl Clover's Cool Big Sis who was converted into his Nox Nictores, Nirvana, by his father in the backstory.
 * Final Fantasy VI -- Terra starts out under Kefka's mind control, and can use special functions of Magitek Armor thanks to her innate magic. The game starts with her being injured trying to escape The Empire and is rescued by Locke. Celes is also this to a lesser extent, and also joins the party after defecting, with the help of Locke again.
 * Front Mission Evolved -- Adela has a very dark history with the E.D.G.E. system  Played With because the hero has a higher aptitude for the E.D.G.E. system
 * Guilty Gear -- Dizzy is the last Gear  and starts out under the control of Testament, but is eventually rescued.
 * Metal Gear Solid 4 Guns of the Patriots -- The Beauty and the Beast squad, and to a lesser extent, the FRO Gs, who were traumatised by war and dealt with it by becoming powered armour wearing cyborgs. None of them become a Love Interest (as if the game would let Snake be happy) but you do have the option of knocking them out instead of killing them (which earns you the ability to disguise Snake as them).
 * Panzer Dragoon Saga -- Azel is one of the last drones left alive, and therefore able to use the ancient technology of the Precursors. She starts out under The Empire's control and fights Edge, but is later freed.
 * Pokémon Colosseum -- Rui can see dark auras around Shadow Pokemon, which is the only way to identify them so they can be snagged and purified.
 * Latooni from Super Robot Wars Original Generation was a member of The School which used a combination of brainwashing and drugs to train Mecha pilots. Bonus points for being a White-Haired Pretty Girl. Slightly subverted in that she wasn't the only student, and there were both boys and girls.
 * Valkyrie Profile -- Shiho was raised from a young age to inspire soldiers to fight harder, but then she crosses paths with the enemy general Suo.
 * Xenogears -- Elehaym, complete with Gundam-style bits.

Web Comics

 * Elf Blood -- SKO and TKO were products of the Council's Project K, a genetic design program to promote the growth of test subjects into supersoldiers who were hyper-compatible with the latest iteration of their Magitek implants. Further compounded by training from childhood for psychic domination and assassination, respectively.

Live Action TV

 * Babylon 5 -- Both of the good psychics are women, while the male psychics either only appear once or are evil.
 * Enterprise -- The  employ a special gifted psychic alien in some kind of neural interface to pilot their cloaking ship  . A major plot point is recovering the said alien.
 * In every generation there is a Chosen One. She alone will stand against the vampires, the demons, and the forces of darkness. She is the Slayer.
 * And Dawn as 'The Key'.
 * While we're on Joss Whedon, River Tam in Firefly and especially Serenity.
 * Max in Dark Angel