With All The Turtles: Raph usually has some sort of love-hate relationship with his brothers, especially Leo, then again all siblings do. He acts so tough out of tough love. He often gets into quarrels with them, and is easily fustrated with Leo's position as a leader, Donnie acting like a know-it-all, and Mikey's lack of maturity. His brothers on the other hand can't stand his temper and his rash decisions. Despite all that, Raph loves his brothers as much as they love him, and he will go to great lengths to fiercily protect them from any sort of harm, especially his two youngest brothers Donnie and Mikey, and he'll always back them up in a fight, especially Leo. Raph had even admitted that he's willing to risk his life, but never the lives of his brothers.
Leonardo: There's usually a lot of tension between the two older brothers, as Leo acts as if he's better than Raph, and Raph has made it his personal goal to prove him wrong. The two are often bickering and clashing over what to do in various situations, as Leo would make some complicated plan, while Raph would just charge right in. They also fight over other stuff, like the Karai situation. Raph can tease Leo with easy as for Leonardo it's complicated for him because he loves his little brother. Their sibling rivalry tends to put a strain on their relationship and at times puts the team at risk. The reasons why Raph doesn't accept his big brother as a leader is because he views himself the strongest, as seen in "Rise of the Turtles", he gets annoyed when Leo ties to compare himself to his favorite character Captain Ryan, a hero from a show called "Space Heroes" which is a show Raph can't stand (and Makes fun of Leo for liking it), Leo willing to be merciful towards badguys and because he feels Leo's plans and decisions are lame. Raph doesn't accept Leo as leader, up until New Girl In Town maybe where he mentions how he needs his older brother. Arguably, Raph might be the closest to Leo. They do love each other, but never seem to make an effort to show it. Though, he did agree that Leo and him are the strongest fighters. Even comforted Leo when his heart was broken by Karai. As seen in "I,Monster" Raph tends to look to Leo for answers, aside from Donnie. Raph and Leo seem to be very close, and they'll always have eachother's back.
Donatello: Raph loves Donnie as a brother, but like the rest of his brothers, gets really annoyed when Donnie starts acting like a know-it-all and starts talking in super-smart techno-babble, and likes to make fun of him as a geek or for his Crush on April. Despite this, Raph doesn't tease Donnie nearly as much as he does Leo or Mikey. Raph and Donnie are complete opposites when it comes to thinking; Donnie often thinks too much and Raph often doesn't think enough. Donnie is Raph's younger brother, even though Donnie's taller than him. He seemed to have low respect for Donnie, along with Mikey, as a fighter as seen in "Mouser Attack!" as him and Leo kept labling them the B-Team and got in their way in when fighting the Purple Dragons or when he declined Leo's idea to contact Mikey and Donnie for help when the mousers attacked them. It wasn't until the near end and dubbed him and Mikey the A Minus-team, which was find considering it was as good as they were gonna get from Raph. Despite that Raph loves Donnie and willing to do anything for him. He has complemented Donnie on some of his findings and when he turned Leatherhead's subway car into "The ShellRazor," Like with all his brothers, Raph is protective of Donnie, and Donnie is willing to assist him the best he can in battle.
Michelangelo: Raph often gets annoyed when Mikey says or does something dumb or silly, and likes to insult and make fun of him. He is seen to guiding his baby brother to somewhat the dark side when it comes to villains like in Never Say Xever where he told Mikey not to apologize for dropping Bradford and Mikey did so. He seemed to have low respect for Mikey, along with Donnie, as a fighter as seen in "Mouser Attack!" as him and Leo kept labling them the B-Team and got in their way in when fighting the Purple Dragons or when he declined Leo's idea to contact Mikey and Donnie for help when the mousers attacked them. It wasn't until the near end and dubbed him and Donnie the A Minus-team, which was fine since it was as good as they were gonna get from Raph, as he playfully gave Mikey a nuggie. Despite all that he cares a lot about Mikey and gets furious, like the other two, everytime he gets hurt by an enemy as seen in "I think his name is Baxter Stockman". He was also the first to show major concern when he realized Mikey was in danger in "New Friend Old Enemy". He was really concerned when Mikey got hurt during the battle with Snakeweed, even giving him a hug. Another example is in Coackroach Terminator, when Mikey was kidnapped by Spy-Roach, as bait, Raph decided to put his fears aside to go save Mikey. Raph, along with Donnie and Leo, even threatened Leatherhead to stay away from him in It Came From The Depths. Raph seems to be very close with Mikey, and is often protective of him as much as he is with the others.
April O' Neil: Raph and his brothers rescue April from the Kraang, but they get away with her father, Kirby O'Neil. They have interacted a little with each other, as seen in Metalhead, so they're pretty good friends. He seems to be quite protective of her as seen in "Panic in the Sewers" where he, along with his father and brothers, were reluctant to let April spy on the foot. In that same episode, He, with Donnie's help, saved her from Dogpound when she was kidnapped. He even paniced when Mikey accidentally spilled the Kraang contaminated water on her, thinking she would disintigrate, but she didn't. Raph though, seems to like to tease her at times, as seen in "The Gauntlet" where he laughed that she was being chased by a giant Pidgeon named Pete. Though he has been willing to help her out at times as seen in "Mouser Attack" where he was willing to help his brothers get April's phone back. Raphael seems to be decent around April, probably since she's the first human friend the turtles have and the fact she's a lady, where he got his brothers to quiet down from laughing at Donnie for getting beat up by a Monkey, when she entered the room. In the LEGO TMNT Raphael short, Raph defeated the Kraang to rescue April hinting that he cares alot about her safety.
Master Splinter: Raph loves Master Splinter as a father and sensei and often tries to prove to him that he's better than Leo. Splinter is aware of Raph's temper and often must give him a guiding hand to keep his anger in check. Splinter can be hard on Raph, especially when he picks on his brothers, but never the less see's great potential in him. Splinter often wishes Raph would think more before reacting when it comes to battle. Like with all his sons, Splinter's very protective of Raph. Raphael loves his father, and showed much concern when he was taken over by the Rat King in "I, Monster." He even gave him a hug when Splinter came back to his senses.
Shredder: Raph and Shredder recently met, and as they immediately saw each other, they knew they were enemies. Raph hates Shredder for, not only trying to kill him, but for harming his brothers and everything he's done to his Father, Splinter. He was the first turtle to suggest that they take out Shredder at the pier in "Enemy of My Enemy."
Karai- He hated Karai from the first moment he saw her. He did try to warn Leo about her, though he did mention to him that he understood how Leo saw Karai was hot (in an evil kind of way). Raph trusts Karai the least considering she's Shredder's daughter, even telling Leo that their chances of her being on their side wasn't really big.
Fishface: Out of all the villains, Raph hates Fishface the most. He fights him every chance he gets. In Baxter's Gambit, they work together pretty well, and seem to be alike due to their aggression and willininess to fight til the end. Fishface even tells Raph about his past. Despite their alikeness, Raph and Fishface are still in a way opposits as Raph fights for those he loves and to protect people while Xever fights to get what he wants or to please Shredder. In mikey gets shellacne before Raph could get seriously hurt by Rahzar, Fishface tackles him into a fight. Fishface could've saved him by choice but didn't let it show. Since he wants the pleasure of destroying Raph himself.
Spy-Roach: Due to his fear of Cockroaches, Raph both hates and Fears Spy-Roach. Spy-Roach also hates Raph, because he tried to kill him when he was a normal cockroach. During the whole episode Cockroach Terminator, Spy-Roach stopped at nothing to kill Raph using Raph's fear of him to his advantage, along with his mutation. Raph spent the whole episode trying to get away from him, but was forced to get over his fear, when Spy-Roach kidnapped Mikey, in hopes of luring Raph out. Raph managed to save Mikey and faced his fear of Cockroaches, fighting the mutant roach, and destroyed him with the drill the Kraang were going to use to drill into the earth's core.
Spider Bytez: Raph and Spider Bytez really hated each other from the moment they first met. Raph despises him because he, as a human, insulted not only him, but his brothers. Spider Bytez, as Vic, took pleasure in tormenting and insulting Raphael, because he got a reaction out of him. When he caught the turtles on tape, Raph wanted to really break his face, but his temper became a problem for the team. Vic hates him because he and his brothers broke his phone and satalite dish. He also blackmails them into giving him a million dollars for the tape. Vic also blames Raph and his brothers for becoming a mutant spider, and attempted to kill the four boys, starting with Raph's brothers, but Raph managed to control his temper and defeat him. For some reason, Spider Bytez calls them kung fu frogs. Spider Bytez is one of the 3 villains that Raph hates, the others are Spy-Roach and Fishface. In a way...Spider Bytez and Raph are alike, due to their temper and being nasty twoards others, the only difference is Vic is just plan nasty and will do anything to get what he wants while Raph just has a slight temper but is willing to fight for the people he loves.
Casey Jones: Raph and Casey clashed with each other as soon as they met, and grew a quick rivalary. That rivalary dissolved into friendship when they were forced to work togther, and actually saved each other from life-threatening danger. Donnie even stated that now they had two Raphael's now.
Spike: Spike is Raph's pet "un-mutant" turtle who he loves and adores. Raphael rescued Spike after he had been flushed down a toilet, and into the sewers. Raphael has a soft spot for Spike which is adorable according to Mikey (and me), and often talks to him about his feelings in private. This is important for Raph as he needs Spike as a sounding board for his inner thoughts and feelings. He can't reveal his feelings to his brothers so he shares them with Spike is an excellent listener and always listens to Raph, even if he can't speak. Spike seems to adore Raph, considering he takes care of him and feeds him his favorite food, lettuce leaves.
When Spike mutates into Slash however, that bond is broken, when Slash tried to destroy Raphael's brothers one by one, in order to grant Raph's wish for a free life. Raph does not approve of Slash's actions, and makes a dangerous foe out of his former pet. In Metalhead Rewired Slash saves Raph from a Kraang sneak attack, showing that, even after their fight, he still cares for Raph.
Irma: It's unknown however in the 1987 series she did seem to be in love with him and boss him around.