Edgeworth and... everyone. Starting with Justice for All, he decides to team up with Phoenix in pursuit of The Truth during court battles but still relentlessly mocks Nick's lack of experience and tendency to just wing it. He constantly berates Gumshoe for overlooking minor details, but has been relying on the good detective's ability to find what other overlook, as well as his tendency to show up at the last second with something decisive. Larry gets picked on relentlessly, but a flashback shows they got on well for the year they shared in school and despite the insults, Edgeworth shows that he still considers Larry a friend. They all show that they're just as capable of shooting a barb back when he gets caught with his pants down. But when worse comes to worse, they're all willing to defend one another at the drop of a hat. The one character he has any kind of regular interaction with that doesn't include a heaping load of biting sarcasm aimed at them is Maya Fey, which might be because of their mutual love for the Steel Samurai franchise. He mellows out after the time skip.
His adoptive sister Franziska Von Karma is quite a bit more on the vitriol part, but Gumshoe is her whipping boy and anyone else that hurts or insults her "Scruffy" will literally be at the end of her lash. Like Edgeworth, she's been working with him a long time (since she started law school at 13). Despite his occasional air-headedness, she knows he got where he is for a reason and recognizes his surprising expertise.
Phoenix has a downplayed version of this with Larry, mainly for Larry's ability to get into all sorts of trouble without trying. Larry's just as willing to point out Nick's screw ups, usually when he misses something even a lamebrain like Larry picked up on.
Athena Cykes and Simon Blackquill, especially in Phoenix Wright: Ace Attorney – Dual Destinies. He constantly berates her for being an amateur who has never taken the spot of lead council on a case, while she treats him like he's a merciless sadist. They're Like Brother and Sister though, and he won't stand for anyone picking on her but himself. Likewise, she'll defend him to the bitter end because despite his dark sense of humor, she knows he's a good person deep down.
The end of Spirit of Justice shows that Apollo and Nayuta are becoming this.
Tomoya and Sunohara in CLANNAD. Sunohara is definitely taking all the abuse, here. Tomoya doesn't really seem to care much one way or the other and most of the 'jerk' part of Jerk with a Heart of Gold comes from interactions with Sunohara. However, he really does care. Sometimes.
In Halloween Otome: Seen with Mr. Bandages and The Count. Their constant bickering is obviously indicative of their deep-rooted affection and friendship for each other.
In Katawa Shoujo, Kenji gets on Hisao's nerves by constantly asking his to loan him money and his misogynist rantings (especially when they're targeted at Hisao's current girlfriend), but there are times when he appreciates having Kenji around, such as when he gets Iwanako's letter in Shizune's route and when he hears that Lilly is leaving for Scotland in Lilly's route.
Hisao and Emi often exchange playful insults in Emi's own route and in her close friend Rin's own.
Icari Isidolde and Kryska Stares from Sunrider have this dynamic. They constantly butt heads about everything from the merits of their respective fighting styles (“Speed!” “Armor!”), to how the course of the war with PACT will unfold, to who had the highest kill count in the last fight. Despite that, the two of them respect each other a great deal, and when push comes to shove they’ve got each other’s backs.
Arihiko and Shiki Tohno. Fighting until they're unconscious is just... well, there's no real ill feeling behind it, it's just what they do. Shiki doesn't even know why.
Arcueid and Ciel are also friends, which you might not pick up on since half the time they're trying to kill each other or something. Count the fact that Ciel is still alive yet isn't going after Arcueid 24/7 proof of Nasu's assurance that they're 'weird friends.'
Without question, this is the relationship between Rin Tohsaka and Luviagelita Edelfelt. While they tend to bicker and fight alot, they are also good friends throughout all the bruising. Honestly, the only thing between them aside from their similar personalities is Rin's boyfriend Emyia Shirou