Warning: Wikipedia contains spoilers
Shinji is a complicated character with many psychological issues. He claims his father abandoned him, but whether this is true or simply Shinji's reinterpretation of his own running away isn't clear. Shinji hates his father. His mother died in an accident during which her soul was absorbed into Eva Unit 01. No one has ever expressed love for Shinji (except for Kaworu Nagisa, the 24th Angel). He runs from his problems rather than confronting them. He has very low self-esteem and often does what others tell him to do. He repeatedly tries to run away from NERV and the horror of piloting the Eva. His friends (especially Misato Katsuragi) try to help him and tell him that running away doesn't solve anything. He appears to learn this by the end of the series, and Episode 26 (from the TV series, not 26' from EoE) shows Shinji psychoanalyzing himself back to relative normality. End of Evangelion also seems to portray Shinji growing out of his problems. These matters should be covered in more detail by more people (in the Talk section perhaps?)
Shinji is the son of Gendo Ikari and Yui Ikari. He is the Third Child and the designated pilot of EVA Unit 01.