For a good introduction into this facet of the show, there's always the lead character, Shinji Ikari. The boy exhibits signs of incredible social anxiety, being completely unwilling to engage in social activities at the onset of the show. In some ways, his politeness and tendency to apologize repeatedly for things that are not his fault, as well as apologizing for his earlier apologies, can also be seen as a link to his performance anxiety. Indeed, throughout the bulk of the show, he exhibits signs of performance anxiety when tasked with piloting the massive bio-mechanical constructs known as “evangelions.” The fact that his social anxiety prevents him from truly opening up to anyone makes it difficult for him to find ways to release his tension and fear, even to his trusted guardian. There are a few fans that have theorized that Shinji's myriad of psychological issues also contains Oedipus complex, though the show merely hints upon this.
An interesting mirror to Shinji is one of the female leads, Asuka Langley Soryu. She has suffered the same trauma as Shinji, mainly the death of the mother and rejection by the father. However, her social anxiety seems to have taken the opposite route as Shinji's, giving her a more extroverted and vocal personality but pushing away people when she subconsciously feels that they are getting too close. She also exhibits extreme status anxiety when piloting the “evangelion” units are concerned. She is highly concerned with maintaining her status as the most effective pilot, going to great lengths to stay that way. However, when the data reflects Shinji's performance as being superior to hers, she goes berserk and insists that such an event is impossible. The situation was worsened when Shinji invariably rescued her, as she was rendered incapacitated by a mental attack that forced her to deal with her myriad of issues, all of which she had pushed under the surface. Her mental health eventually collapses in the wake of those events, causing her to rapidly progress from self-doubt, to depression, and finally to a complete mental and emotional breakdown. In the original incarnation, she never actually recovered.
In some ways, Shinji's guardian, Misato Katsuragi, has also experienced stunted mental health. The death of her father traumatized her, such that she was unable to speak for several years after the incident. Her attraction to a co-worker, Kaji, is an overt sign of Electra complex. Characters within the show have pointed out that Misato's attraction to Kaji stems from his resemblance to her father, both in appearance and personality. She has also exhibited some signs of separation anxiety, as evidenced by her unwillingness to sacrifice Shinji in battle, even if it would cost potentially thousands of other lives to save him. Her constant worrying over this fact is taken as evidence of the problem. Her outgoing and happy personality is also hinted to be her way of coping with some form of social anxiety, which manifests by her refusal to allow herself to get emotionally close to her. It is also implied that she understands this, as she notes that any attempt to develop her parental relationship with Shinji would only result in both of them getting hurt. Even the parental nature of her relationship with Shinji is questionable, particularly due to her statements implying that she will sleep with him if he does as she says and saves the world in the “End of Evangelion” movie.
Rei Ayanami, another of the lead characters, is generally viewed as a “poster child” for a number of stunted mental health. She is often seen being incapable of feeling emotions, or at least incapable of expressing the emotions she feels. However, this lack of emotion from her has only added to the speculation on what her myriad of psychological issues are. She exhibited Thanatos, the so-called “death instinct,” on one occasion. Her lack of friends and social contacts has been interpreted by some as being a product of her own social anxiety, which is in turn aggravated by her apparent lack of emotions. Indeed, it is generally assumed that the other students tried to initiate social interaction with her, but that she herself prevented it from going further than that. However, unlike Shinji and Asuka, she does not seem to exhibit anxiety problems regarding her ability to pilot an “evangelion,” though whether this is because she does not feel it or she is incapable of expressing her frustrations is debatable.
All of the other major figures in the show exhibit signs of mental health problems in most incarnations. It has often been stated that the characters are motivated and controlled by their anxiety disorders and psychological issues, with most of them being where they are because of their problems. The anime was heralded as revolutionary because of its psychological and religious themes, as well as showing that the mecha sub-genre could have a deeper meaning than “giants robots fighting other giant robots.” The point is arguable but, even a decade after the show was first released, it is arguable that no anime has had characters as psychologically warped as “Evangelion.”