This page lists all of Jimmy Orange's relationships with other characters throughout the series.
Henri Orange is Jimmy's dad, so they share a close bond. Jimmy usually outsmarts Henri in various situations, but also may look up to him, as he wanted to learn how to save a princess from Bad Jack's tower the "Old-Fashioned way", as he didn't want to risk losing anything else with one of his "fresh" plans. Henri also may look down to Jimmy for a "fresh plan" when needed.
Princess Cat is often like a sister to Jimmy. They share a close bond and enjoy fighting together. Usually, whenever Jimmy's obsessive side takes over something, Cat is always there to bring him back to reality. They often look out for each other and help each other out of situations, such as Cat coming to rescue Jimmy when he and Lance are trapped in Bad Jack's cage, and Jimmy sneaks Cat out of Princess School to fight Madame Witch. However there is possibly a romantic relationship with Jimmy and her that may be revealed in future episodes.
Not much is known about the relationship between Jimmy and Kurt, but in How to Save a Princess, Jimmy puts something in Kurt's sandwich, possibly an emetic, knowing Lance would take it, as he did in the beginning of the episode. This could mean that Jimmy and Kurt are somewhat friends.
Villains in general
Jimmy generally dislikes any villains and always comes up with a "fresh" plan to defeat them (or trick/manipulate them) when on an adventure/mission.
Jimmy and Bjorn share a pretty good friendship. In The Helmet of Epic, when Jimmy wants a new helmet to replace his old helmet, he calls up Bjorn for any spare helmets. Bjorn decides to go through his father's treasure, despite the possible upcoming consequences for a new helmet for Jimmy. After he gives it to Jimmy, he considers Bjorn a best friend. In Treasure Trap, he and Jimmy are shown to have a close bond, despite both their parent's disapproval that humans should be friends with dragons. In The Dragon Rider, Jimmy will pretend to be Bjorn's trainer.
Jimmy and Torpedo share a well human-to-animal relationship. Jimmy presumably doesn't know how to ride Torpedo, so he rides a sidecar attached to Torpedo whenever his dad is riding the horse.
Jimmy and Lance generally dislike each other. Lance usually considers himself superior to Jimmy, and constantly bullies him. Despite their rivalry, they must work together whenever one of their relatives (Wilfred and Henri) are in trouble.