Natsuki Subaru
After being saved by Subaru, Rem develops feelings for him. She tends to be aggressive in her approaches, often asking him to praise her, and will do anything for him, such as turning a blind eye to certain actions. Later, they semi-seriously agree that if Subaru can persuade Emilia, then he will make Rem his second wife, and Subaru even confesses to her in both the web and light novels. Nevertheless, Rem suffers in battle and falls into a coma before Subaru manages to tell Emilia about their idea.
Ram
Throughout their childhood, Ram had always been superior to her in every way. Growing up in her sister's shadow, Rem greatly admired her older sister, but also had some lingering resentment and feelings of self-inferiority. However, that resentment turned into guilt after Ram lost her horn. Even afterwards, Rem still believes that her sister is much greater than what she can ever achieve.
In general, Rem and Ram are as close as expected from the twins. For example, although they have quite different personalities, the sisters easily understand each other and even instinctively synchronize their thoughts or actions, if necessary. This is particularly noticeable on Rem's part, who has a platonic sister complex towards Ram and is even openly jealous of her to Subaru when she thinks they are in love with each other.
Roswaal L Mathers
Roswaal took Rem and Ram under his wing and is shown to deeply care for them, as seen when Rem died of unknown causes and he immediately suspected Subaru for her death (he was even prepared to kill him, much like Ram).