Rei, like Hotaru, isn't much of a talker.  Mostly reserved, she just appears to do her job, and then she's off.  There is a sense, though, that the real Rei is trying to get out.  Shinji somewhat opens her up a little, while Asuka trashes her whenever she can (She hates Rei because she's "passive, like a doll".  I could explain what that means, but I've already said  too much and I don't wanna spoil more of it away.)