On a more serious note, as much as Rem is lovable and loyal, I find her relationship with Subaru rather disturbing.
We know Rem has confidence and self-worth issues because of her history with her sister: When they were young, Ram helped her with everything and was better than her at everything. In a moment of weakness, Rem felt relief that Ram having her horn cut off meant that Rem would no longer be overshadowed by her sister. As penance for her weakness and for repaying Ram's help, she more or less dedicated herself to helping Ram.
Her relationship with Subaru seems almost like an eerie replay of what happened with Ram. Of course, Subaru did not do nearly as much for Rem as Ram did, but she seems to greatly value what he did--trying to save her and affirming her worth as an individual. And her behavior seems at least partly attributed to her moment of weakness--when Subaru pushed her from the dogs, she thought she could have pulled him to safety, but she hesitated and did not. It was penance for that act that drove her to go into the forest for herself, and I do not think she ever let go of that--which was why she identified Subaru as the reason for her to die when she entered the cult headquarters.
In effect, Rem simply acquired another person she felt that she had to dedicate herself to. it is quite similar to what happened with Kaede in
Shuffle, and it is about as unhealthy, even though she has not shown any yandere actions toward Emilia.
As for Subaru, Rem dedicating herself to him seems to reinforce the notion--whether he really believes it or not--that he is owed something for saving them. In a way, the argument between Emilia and Subaru at the end of episode 12 was perhaps less a meta discussion about RPGs giving the hero the heroine as a reward than a warning about Subaru and Rem: Their relationship is not heartwarming romance; it is actually unhealthy co-dependence.
Given Subaru's mental state, I wonder if he will try either of the following this loop:
1. Save only Rem and drive the 2 apart when he reveals to Rem that he deliberately abandoned Ram.
2. Try to use Rem as a living weapon.