Harbinger of Tragedy
First Children, destinated pilot of EVA-00
Pilots of the Evangelions are called "Children." The word is always in the plural, even when referring to a single person. When the series was brought over to America, ADV (which licensed the anime) changed it to "child" in the single term, but Gainax prefers the plural form of the word, so I'll be sticking with Gainax on this. Rei is the First Children, meaning she is the first person identified by the Marduk Institute, which is in charge of selecting candidates for Eva pilots, to be a suitable pilot. She is present in much of the early testing phase of the Evas, being the pilot to sit through start up tests and many of the dangerous tasks that comes with being assigned to the prototype, EVA-00. As shown by the first episode, Rei is often injured due to her position as a pilot.
Unlike Shinji, who is basically a newbie, Rei is pretty seasoned. And also unlike Shinji, who often fights based on emotions, Rei fights almost exclusively on orders alone. She is the perfect example of the obedient subordinate, listening to Commander Ikari's every order, something that bugs Asuka, the Second Children, to no end. Rei's determination in battle, unlike Asuka's (which is based on pride), is more based on her sense of duty. Piloting Eva is all Rei seems to do with her life as she does not have any hobbies or friends (until Shinji comes along).
Her relationship with Unit 00 is quite rocky. It took her months to properly synchronize with it, where as Shinji did it his first time. During one of her activation tests, Unit 00 lost control and went berserk with her inside, eventually ejecting her entry plug violently from its back. The most likely reason for their lack of unity is due to Rei's emotional void. The souls within EVA-01 and EVA-02 are the souls of Shinji's mother and Asuka's mother, respectively, but Rei has no mother. The soul inside EVA-00 is never revealed, but there are theories. One is when Akagi Naoko died, her soul was placed in this prototype, which might explain the hatred Unit 00 aimed toward Ikari Gendou behind the viewing window when it went berserk, and similarly when Shinji test piloted Unit 00 and it saw Rei behind the viewing window. The other theory is a fragment of Rei's own soul (Rei I) was placed inside Unit 00, rendering it less stable because of its difference. Both have its gleam and its holes, but the Akagi Naoko one seems less popular amongst fans.
Besides strictly following orders, Rei has a habit of putting herself at great risk during battle. She uses her body (and that of Unit 00's) almost as sacrifices, once charging without any weapon except a N2 bomb in hand at an Angel. Rei acts as though she has no fear of death, saying, "even if I die, I can be replaced." One can look at this as a sign of recklessness or self-worth, but I think her attitude is more revealing about her existence at the hand of Ikari Gendou than just a suicidal streak.
Rei also has a habit of making herself out to be some martyr. During the battle against Ramiel, the Fifth Angel, Rei uses herself and Unit 00 as shields for Shinji as she shoots at Ramiel, staying until Unit 00's outer armor had nearly been melted off. During a blackout, fighting against Matariel, the Ninth Angel, when the three Children discuss tactics, Rei is the first to volunteer for the most dangerous position, but Asuka takes it instead.