These are the relationships Carrie has with the other characters in the series.
Carrie is revealed to have a strong relationship with her father. In "The Mirror," she shows genuine sympathy for him when she sees what the curse and loneliness had turned him into. She also takes offense when Gumball repeatedly insults her father. When they finally succeed in breaking the curse and freeing him, the first thing they do upon being reunited is embrace in a long hug.
Carrie seems to be on good terms with Darwin, who was the first to suggest using Gumball's body in "The Ghost." In "The Flower," Carrie and Leslie use Darwin's body as a shield from incoming projectiles. In "Halloween," Darwin kisses Carrie immediately after becoming a ghost, revealing that Darwin has had feelings for her for some time. To which she reacts with a blush, implying that she does have feelings for Darwin as well. She and Darwin are later seen back to back during his musical number in "The Words," but despite Darwin's implied interest for her, she runs off after he refers to her as "one more emo freak."
In "The Scam," their feelings for each other are much more heavily implied. Gumball uses the thought of getting closer to Carrie in order to tempt Darwin into following through with their scam, leading to Darwin briefly fantasizing a romantic moment with Carrie. Then, when she requires a body to possess in order to eat the candy they gathered, she sheepishly asks Darwin to borrow his, causing him to get nervous as well. At the end of the episode, they both awkwardly try to find an excuse to get the other to hang out with them.
In "The Matchmaker," Carrie continues to show romantic interest in Darwin, and even admits her feelings to Gumball. However, she is very disappointed when she finds out that Darwin supposedly does not like her anymore and likes Teri instead. Though jealous at first, she reluctantly brews a potion that will make Darwin and Teri fall in love, as she only wants to see Darwin happy. However, once Gumball realizes that Darwin never liked Teri to start with, and never abandoned his feelings for Carrie, the two set out to separate them without progress. Finally, Carrie concedes and begins to cry at the thought that she has lost Darwin forever and disappointed that she didn't act sooner. Fortunately, her tear, being a sign of love, breaks Darwin's spell. Encouraged by Gumball, Carrie asks Darwin out on a date, which he gladly accepts and they share a kiss.
In later episodes, they are shown acting as a couple, revealing that they are officially dating.
Carrie and Gumball are close friends. In "The Ghost," Gumball allows her (somewhat reluctantly) to use his body so she could eat large amounts of food. When Gumball refuses to allow her to use his body near the end of the episode, she attempts to forcibly take it, resulting in a brief struggle. However, the two quickly reconcile and seem to be on good terms from then on.
In "Halloween," Carrie takes Gumball to a ghost party. When things got out of hand, she starts getting deeply concerned about his safety, spending the entire night looking for him instead of partying. At the end of the episode, however, with Nicole glaring at her, she quickly abandons him in embarrassment.
In "The Scam," Carrie and Gumball scam the whole school into thinking it was haunted in order to get candy. She also helps him and Darwin get rid of Gargaroth and is even willing to sacrifice herself for their safety.
In "The Matchmaker," Gumball enlists Carrie to assist him in hooking Darwin and Teri up despite her disdain on the matter. However, once he realizes his big mistake, he's determined to make it up for her, playing a major role on hooking up Darwin and Carrie, consequently being saddened upon seeing how the opposite is achieved and the progressive negative effect this has on her. In the end, when Carrie finally gets together with his brother, Gumball is undoubtedly happy for the two of them.
In "The One," Carrie is targeted by Tobias in his "elimination plan" because she's one of Gumball's five closest friends. It would appear that after Darwin, Gumball considers Carrie his best friend.
Carrie and Penny seem to be friends, as they were both seen hanging out in Molly's treehouse in "The Pressure." At the end of "The Flower," though, Penny gets possessed by Jealousy and angrily insults Carrie when she addresses Gumball at the end of the episode, although the effects were most likely caused by Jealousy and not actually Penny. They are also seen hanging out together with the other girls.
Carrie seems to have a slight friendly relationship with Banana Joe, as in "The Return" they are sitting together, but not much else is known besides that.
Carrie seems to be good friends with Rachel as they are seen chatting in "The Third." Not much else is known about them otherwise.
Carrie seems to be friends with Leslie, as they have been seen talking and being friendly towards one another. She also seems concerned about him as he was being victimized by Jealousy in "The Flower."
It seems that she might be frenemies with Tobias as well, as they could be seen hanging out a few times, doing things like playing football on the playground and so on. However, at other times Carrie appears to find him annoying.