A Mother's Love - Rei, Yui and Shinji
All right, so Rei is partly cloned from Yui, Shinji's mother. That may explain to some length why the distant, uncommunicative girl who usually shows little response to anyone's overture of contact cares about Shinji. But is that Rei caring for him, or Yui? This is my opinion, remember - you are free to have yours.
Shinji may have recognized something belonging to Yui when he sees Rei (although that's open for debate), memories triggered from his early years with Yui. (Don't worry, I'm not going psychological here. Not very, anyway) When he watches Rei squeezing the washcloth, for example. Or after he has been rescued from Leliel. In the hospital, Rei spoke the very same words he has remembered Yui saying, when he was still trapped inside Leliel, "Yokatta wa ne (That was good)." But whether or not Shinji attaches much significance to this is unclear. Shinji is depicted to show the strongest realization at the end of the Third Impact. As Rei's physique falls apart, Shinji sees Yui's image drift away from him and thinks, "What are you going to do now, Mother?"
In return, Rei senses a bond between her and Shinji that she cannot explain. Again, whether or not she fully realizes this is also unclear - you know how Evangelion is. But Rei II goes as far as self-destructing Eva-00, and herself with it, when Armisael attacks, so that Shinji will be saved. Rei III, her successor, shows the same faint realization, if in a slightly different way. She confesses to having forgotten saving Shinji, but later she rebels against Gendou when he tells her to "bring Yui back to [him]", because she says, "Ikari [Shinji] is calling."
This is not to say Shinji is in love with Rei or vice versa, only that they care for one another in a degree. Asuka is Shinji's mate (objections anyone?); Rei is Shinji's guide in discovering courage and self-honesty.
So it appears that Shinji and Rei shares something after all, however vague. Shinji, never the most open of people, feels imperceptibly drawn to the remarkably reserved girl. As for Rei, despite being a clone, she knows her own mind when it comes to Shinji, which is particularly true of Rei III. Is that Yui or Rei, though? A bit of both is my opinion.
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Shinji may have recognized something belonging to Yui when he sees Rei (although that's open for debate), memories triggered from his early years with Yui. (Don't worry, I'm not going psychological here. Not very, anyway) When he watches Rei squeezing the washcloth, for example. Or after he has been rescued from Leliel. In the hospital, Rei spoke the very same words he has remembered Yui saying, when he was still trapped inside Leliel, "Yokatta wa ne (That was good)." But whether or not Shinji attaches much significance to this is unclear. Shinji is depicted to show the strongest realization at the end of the Third Impact. As Rei's physique falls apart, Shinji sees Yui's image drift away from him and thinks, "What are you going to do now, Mother?"