Three of Me, One of Someone Else
The rebirth of Ayanami Rei
In the series, there are three different Ayanami Rei we meet. Fans call them Rei I, Rei II, and Rei III, after the episode titles and OST track names. Because she is a clone of Ikari Yui, Commander Ikari most likely wanted to guarantee her survival, so he can carry out his own selfish plans. The spare parts for Rei in the Dummy Plug System must have been there to ensure she would keep on living. From Rei III's behavior after she replaced Rei II, they do not share all of their previous life's memories.
Rei I was the child Commander Ikari brought with him to Gehirn (NERV before it was NERV) under the guise of a friend's daughter. Her personality seems much more deviant than the later Reis, as made clear by the way she childishly taunted at Akagi Naoko using the name Commander Ikari calls her. That mistake would result her in death by strangulation at Dr. Akagi's hands. Rei I acted perhaps her age, taunting at Dr. Akagi because she had a secret to tell. Would this Rei (I) have grown up to be the stoic and socially inept Rei (II) she would be replaced by? We can never know for certain.
Rei II is the Rei we are most familiar with and the Rei who was an Evangelion pilot. She receives the most development through the series, growing from the distant and emotionless girl she initially appeared, to the girl who eventually opened up to Shinji and bonded with him like she had never done before. Rei II went from not even getting embarrassed when Shinji accidentally fell on top of her naked body to someone who blushed when Shinji commented on how she seemed motherly. It was this Rei who would eventually sacrifice herself by self-destructing Unit 00 to save Shinji from the Sixteenth Angel, Armisael.
Rei III replaces Rei II after the battle against Armisael. Shinji is exuberant to see her alive, thanking her for saving him, but she shows little recollection of the incident and says, "I think I am probably the third one." This shows she is aware of her "rebirth" after being killed. Her personality, though, seems to have reverted back to how it was before she got close to Shinji. In The End of Evangelion, however, she displays a preference toward Shinji over his father, Ikari Gendou, which is only possible because of the bond they developed through the series. I think she carries the feelings Rei II had inside her, but not the specific memory of why or how things led to those feelings. She knows objects from Rei II's life, but she doesn't understand how she knows them, and she cries for the first time, even though she feels it is not the first time she's seen tears; the first time was when Rei II shed tears during the battle with Armisael.