Ikari Shinji
As the main character in Neon Genesis Evangelion, Shinji was appointed as one of the Three Children (the Third Qualifier), to pilot the Eva-01. He has a very low self esteem, and  therefore has a very hard time expressing his feelings because he fears having them hurt by others. He has a poor relationship with his father, Gendou Ikari, and his mother passed away when he was still at a very young age. He met Misato Katsuragi at Tokyo-3, who became his roommate and guardian. I agree with a lot of people.  Shinji is a jerk, but what can you expect from a kid who was abandoned by his father when he was a little boy?  And besides, I know that he's a little hysterical at times but he is just wondering what most people ponder... Why are we here, in this place filled with hatred and hurt?  It's a simple question, so that we may also have happiness.  without hate and hurt there's no pleasure and happiness.  Shinji just saw the negative parts of everything.  He never gave any thought about all the people who love him and care about him.  He's like some one who only sees one side of the moon and thinks that it's a flat circle that's white.

Ayanami Rei 
Ayanami Rei is a clone of Yui Ikari, Shinji's mother.  Gendo Ikari, Shinji's father, keeps many clones of Reis in the Terminal Dogma, in case Rei dies.  Rei has died two times already.  Her first death was brought by Dr. Akagi Naoko.  Her second death was during the 16th Angel.  So the most recent Rei is the third one.  Her soul is also derived from Lilith.  In the movie she combines with Lilith and handed the future of mankind to Shinji Ikari, therefore betraying Gendo Ikari.

Sohryu Asuka Langley
The Second Child from Germany, Asuka Langley is filled with pride and confidence as she tries to be the best Eva pilot in NERV.  She has already achieved being the most popular and Hottest girl in school.  She has this problem of wanting to live alone though.  It's in her thoughts. she doesn't want to be taken care of and wants to do everything her own way.  She hates everyone as she has quoted in many episodes.  But at the same time, she hates this loneliness and wishes to be taken care of.  It's one of these conflicts within herself.  She eventually goes crazy because she keeps on getting defeated by Shinji and Rei.  And the Unknown beam the Angel, her tormenting pass all flashbacks to her and her mind and soul goes into total meltdown (exaggerated).

Katsuragi Misato
Misato is the Evangelion pilots' main superior officer.  Responsible for the operations of the whole NERV headquarters whenever the commander is not present, Misato has only one goal in life: to destroy the angels that killed her father during the Second Impact.  His death caused her great mental trauma which led to a long period of agnosia (loss of speech). Misato during the course of the series became Shinji's guardian, caretaker figure.  An attractive woman with a cheerful, optimistic personality, Misato is also the only living human being to witness the Second Impact first hand and to have survived.  She, in Fuyutski's terms witnessed hell. With information provided by Kaji, Misato is also in search of the truth behind Gendo.

Gendo Ikari
Gendo Ikari, the person who is in charge of NERV headquarters, he is a jerk.  Everyone knows that.  He treats Shinji like nothing, even though he is his son.  I mean, Gendo treats Rei better than Shinji.  The reason why is because he is afraid of being hurt again, like when his wife Yui died.  Well..... why is he so close to Rei then, because he has a Terminal Dogma filled with her clones just waiting to be used.  So that's why he abandoned Shinji in the first place.  He doesn't want to get too close to him, so when Shinji dies, he won't suffer as much as he did when his wife died.  I don't know about u but it's starting to make sense to me.

Suzuhara Toji
Toji is one of Shinji's friends, even though the first time they met he punched Shinji hard.  He eventually gets chosen as the fourth child to pilot Eva 03, the new Eva made by the Americans.  Everyone knew that Toji was going to pilot Eva 03 except Shinji, and in the end, it's Shinji that has to fight Eva 03 after it gets possessed by an Angel.  Eva 03 gets taken over by an angel and tries attack NERV headquarters.  It has more agility and strength than the original Eva, especially after being controlled by an Angel.  Eva 03, with Toji trapped inside it was soon destroyed by Eva 01 (after Shinji refused to fight and Eva 01 was turned to dummy piloting).  Luckily, Toji survived, even after Eva 01 crushed the Entry Plug... Lucky Bastard. 

Angels 
Angels are enemies of mankind which can appeared in various forms. Nothing about them is known, even whether they're living things or not. They possess AT Fields in short) which can "neutralize" attacks by normal weapons. Even if the Angels are partially damaged by extremely powerful weapons, it has the ability to recover any damage. Thus, the only way to destroy them is to attack after "neutralized" its AT Field.

Evangelion
Also called "Eva" in short, Evangelions are humanoid "robots" designed to fight against Angels. They can generate its own AT field, and can carry weapons which "neutralize" the AT field of Angels. They are very expensive to build and maintain. Plus, they are cumbersome to operate. They need external power in order to fight for a long period of time. They can only operate maximum of 5 minutes without the external power source.