Shinji Ikari
Shinji Ikari is the Third Child, the main protagonist of the series and the designated pilot of Evangelion Unit-01. He is the son of Gehirn bioengineer Yui Ikari and NERV Commander (formerly Chief of Gehirn) Gendo Ikari. After his mother's death, he was abandoned by his father and lived for 11 years with his sensei, until he was summoned to Tokyo-3 to pilot Unit-01 against the Angels. He lives ini tially just with Misato Katsuragi; they are later joined by Asuka Langley Soryu.
Personality
Shinji initially shows a passive and laid-back personality, inheriting such traits from his relaxed life with his sensei. When he is told to pilot Unit-01, he denies, not wanting to do it. Though Shinji denies it, he yearns for praise, and he eventually begins to pilot Unit-01 to gain the approval and love from his father. He also continually tells himself "I mustn't run away!", further demonstrating his need to move forward and let go of the past.
Shinji shows a great fear of emotional pain and of being hated or left behind, likely due to his perception of being abandoned in his youth and, subsequently, blaming himself for not being good enough to make his father stick around. In general, Shinji is shown to be introverted and disconnected from physical reality due to having little to no meaningful contact with others. In social party situations, he is shown to be quite uncomfortable, and he often has difficulty controlling his emotions around others due to his hard time letting go of the past. He is shown to the extreme of this, forsaking many lives (even his own) to save one person.
Due to Shinji's high nostalgia and fragile emotional state, he chooses to shut out the world, as evidenced by the headphones he wears rather often, plugged into an SDAT music player. Through all this, Shinji is also aware of his own faults, has a detailed memory of the past, and generally is outwardly gentle. He is the only one who tries to find a reason to fight the Angels, and sometimes his justification for fleeing from piloting is to avoid hurting others.
Relationships
Asuka Langley Sohryu
Shinji is attracted to Asuka, though the reasoning is not explicitly stated. It might be that her bullying sometimes causes Shinji to bite back at her, as Asuka wants his attention, and he views Asuka, in a strange fashion, as a source of strength, one that he misses when Asuka is laid low by her encounter with Arael. However, Shinji directly expresses his feelings for Asuka by trying to kiss her as she sleeps, when he masturbated at the accidental exposure of the then-comatose girl's breasts, and in the Episode 26 Instrumentality sequence when he says "I want to help you somehow and be with you forever.", and Asuka states she wants Shinji all to herself and that she is not only aware of his masturbation at the hospital, but also implies that it is, in fact, a habit of his. In Episode 22, Asuka laments that Shinji "won't do anything, won't help me, won't even hold me.", revealing Asuka's frustrations at Shinji not picking up on her advances, particularly earlier in Episode 9 and their kiss in Episode 15, despite him barely understanding them. Asuka also seems very jealous of Shinji's interactions with Rei, which furthers her antipathy at her.
This is also paired with Asuka eventually letting go of seeking Kaji to validate her as an adult, as she starts to begrudgingly accept Shinji's piloting prowess and to find an equal in him, something she is unwilling to do with Rei. After Episode 16 however when Shinji surpasses her synch scores, she starts resenting his success as in her view, Shinji hasn't worked for it whereas Asuka spent her whole life training for piloting Eva and she is unsure of how to deal with not being the best. Asuka's expectations for Shinji as a strong male, that she used to project on Kaji, clash with the reality of him as a "housebroken male", despite him being much more than that: Asuka believes Shinji is unwilling to help her, in combat or otherwise, despite him showing bravery even without request - like when he rescued her from the volcano in Episode 10. Additionally, Asuka interprets Shinji's inaction during their kiss in Episode 15 not as lack of understanding, fear or insecurity, but as conscious rejection, which she greatly resents.
Despite Asuka's own abrasiveness toward Shinji, she develops a rather skewed mentorship with him. It is her constant battling, coupled with her seemingly unquenchable energy, that often gives Shinji strength and confidence he didn't know he had. During the days that they lived in a furnished room at NERV HQ practicing their dance routine, Shinji began to understand where Asuka was coming from and allowed himself to confide a little in her. In the end, it was her perfectionism which awakened Shinji's confidence, allowing them to synchronize and defeat Israfel. Asuka's ambivalence regarding their mutual feelings often confuses Shinji, leaving him unsure as to what he feels for her, as Asuka, in order to avoid intimacy forming between them, sometimes reverts to her self-defense mechanisms, and pushes Shinji away, even if Shinji seems barely affected by those, as per his passive nature he seems content to merely have her attention.
Rei Ayanami
Shinji first encounters Rei at the Nerv HQ in Episode 1, after being summoned by his father regarding the oncoming Angel attack. Despite being heavily injured, Rei insists on piloting the Eva when Shinji protests against getting in the robot, eventually forcing him to face his responsibility. She is shown as a practical and mysterious figure, acting solely on commands and refusing all social contact. Shinji is initially puzzled at Rei's behaviour, and the bond she seems to have with Gendo, in contrast to Shinji's own and much more strained relationship with his father. Through his persistent efforts to befriend Rei however, she ends up opening up somewhat to him and realizing more about herself and her role in the Human Instrumentality Project.
The extent of Shinji's attraction to Rei is unclear even to him; certainly, it is of a different sort than his sexual and seemingly romantic attraction to Asuka. It is implied that he is drawn to the vestiges of his mother that lie within Rei. As they grow closer, their relationship is a source of both joy and pain for both of them. It should be noted though, due to being genetically related to Rei's ultimate fate, the two may never have a romantic relationship, or even wish for one. Rei also seems to associate Shinji with Gendo with some level, implying she might also feel a form of familial connection with him. Shinji relates to Rei's sense of isolation and loneliness; it is not until Shinji is absent that Rei begins to understand that she was in fact feeling these things. She comes to realize that she wants to protect him, and in the battle with Armisael, she self-destructs to save Shinji. After Rei comes back as another clone, Shinji becomes alienated from her, however, in End of Evangelion she decides to hand control of Instrumentality to Shinji instead of Gendo, and gives him the choice to accept or reject it. She is last seen in her Quantum form briefly watching Shinji just before he notices Asuka on the beach. Anno has described Rei as Shinji's unconscious self.
Rei has a much stronger bond to Shinji in the manga and their relationship has far more development, as Rei is greatly impacted by touching Shinji's hands and as Armisael attacks her, she realizes she has feelings for him she cannot understand. She also realizes she is jealous of Asuka dividing Shinji's attention. However, she is absent from the ending. While Asuka was as a symbol of "heterosexual desire", Sadamoto designed Rei as a "mother figure", thinking of her as "the Yin opposed to Asuka". As such, he decided to give Rei more room in the manga, emphasizing Rei's maternal role. Perhaps alluding to them having a sibling relationship instead of a romantic one, official material states Gendo intended for his biological daughter to be named Rei had Shinji not been born a boy.