Jorge the conquistador Sanchez member and Carmelo the native Mesoamerican Sanchez member from The Book of Life, have a rather complicated relationship with each other. The former often calling the latter savage and the latter unintentionally bumps around the former. Not surprising considering the complicated history between the conquistadors and Mesoamericans. They're still family though.
The Boys in the Band. Michael and Harold. While it isn't clear they are best friends, two moments reveal their deep relationship: Michael's gift to Harold, and Harold's quiet assurance after giving him a "The Reason You Suck" Speech "I'll call you tomorrow."
Dante and Randall from Clerks. They both argue about things all the time and snark at each other (especially Randall, who seems to enjoy messing with Dante), but when it's all said and done, the two are almost inseparable buddies. Jay and Silent Bob have a similar dynamic, except Jay does most of the talking and Silent Bob ignores it with an air of sarcasm, despite not saying anything.
Bartleby and Loki in Dogma (like Jay and Silent Bob, who they share the screen with) are unquestionably vitriolic.
Loki: All lines... are currently down. Bartleby: Okay, I'm gonna have to Loki: Would you just knock it off! Bartleby: Hey, you're doing it again, now stop Loki: Fuck! Bartleby: what did we talk about?
Michael Patrick Donovan and Thomas Aloysius Gilhoolie from Donovan's Reef: World War II buddies who share the same birthday and make sure they get together every year to punch the crap out of each other.
Sam French and Jake Wyer in 50/50 have this in spades, although Jake likes to pretend he can't stand Sam.
Forrest Gump doesn't see it, but Lt. Dan has a lot of anger towards him and generally treats him with contempt. But underneath it is an appreciation that Forrest holds no grudges and will do anything to help a person in need. By the end, there is no doubt they are best friends.
In Guardians of the Galaxy, this Trope could describe the relationship between pretty much any two members of the team (except Groot, who's friendly to everyone), but especially between to Drax and Gamora. In one scene, the former calls the latter a whore and then a few minutes later shoots Nebula with a rocket launcher when she is talking trash to Gamora and planning to attack her.
Kiss Kiss Bang Bang has Harry and Perry. Harry is sure that Perry is really his friend, and somehow ends up being right. Harry would give as good as he gets, except he's a colossal ditz and no-one can out-insult Gay Perry anyway.
In The Lord of the Rings trilogy, Legolas and Gimli are portrayed in this manner. Basically Legolas is Bugs Bunny and Gimli is Daffy Duck. As much as Gimli was exasperated by Legolas and as often as Legolas would act smarmy towards Gimli, the two always ended up being there for each other. This is an exaggeration of a similar relationship in the books.
Gimli: "Never thought I'd die fighting side by side with an Elf." Legolas: "What about side by side with a friend?" Gimli: "Aye. I could do that."
In Made, the two main characters are best friends from high school, but they bicker almost nonstop due to Bobby's short temper and conservative approach in contrast to Ricky's loud, reckless and unreliable personality.
In The Magnificent Seven (2016), Faraday and Vasquez spend most of their time frequently insulting and trading derogatory racial jokes between each other, but eventually became very close friends, as seen when Faraday was shot by one of Borge's main henchmen, Vasquez guns the henchmen down vengefully while screaming curses.
In My Girl, Vada and Thomas J are best friends and throughout the movie, Vada can be seen fighting with him and other times she is seen having fun with him. All in all, Vada cares deeply for Thomas J.
Will Turner and Jack Sparrow. The principled blacksmith and scheming pirate are frequently at loggerheads, but in the first movie Will risks everything to rescue Jack from the gallows, and in the third, Jack sacrifices immortality to save Will's life.
Sherlock Holmes and John Watson in Sherlock Holmes (2009). Watson always remarks Holmes is too much for him to handle and constantly tries to get out of joining him on his various jaunts, yet invariably they end up working together because Watson likes the chase almost as much as Holmes and they are in sync during investigations, whether or not he wants to accept it.
Donkey and Puss In Boots from the Shrek franchise are like this. As the films went on they become closer allies and best friends but would still bicker and fight over being Shrek's best sidekick.
'Donkey': I'm sorry but the position of "annoying talking animal" has already been taken!
Luke's relationship to Han Solo. Especially when they're arguing over Leia.
R2-D2 and C-3PO qualify as well.
Stroker Ace and his chief mechanic Lugs. They argue back and forth about little things and criticize each other's habits. They also team up in bar fights and work together to help Stroker out of his unfair contract. Best seen when Lugs , mistakenly thinking that Stroker forcibly slept with Pembrook, hunts Stroker down and punches Stroker in the face. Neither one mentions the incident at all, continuing on like it never happened.
In Teenage Mutant Ninja Turtles (2014), Raphael is constantly at odds with Leonardo, hates being told what to do, and mentions that he's leaving the group the first chance he gets. However at the end, he defers to Leo's leadership and tells the others to do the same, as well as confessing that he says he's leaving because he's really just scared that he's not as good as them, and he only says that to make them bond harder when it feels like things are driving them apart.
Tommy Boy: Tommy Callahan and Richard Hayden spend much of the movie trading insults with each other, but when the chips are down, they have to admit that they consider each other friends.
In What a Carve Up!, Syd and Ernie spend a lot of time insulting each other. However, when the chips are down and there is a madman running around the mansion offing the guests one by one, they've got each others backs.
It's implied that Nick and Finnick's relationship in Zootopia is pretty much this as they are business partners...who constantly tease, insult, and even threaten each other. However, Finnick did help Judy find Nick near the end, which also implies, as much as he threatens him or laughs at him, he does somewhat care about him.