The Jake & Amir sketches from College Humor are built on this trope. Amir is usually the one who is annoying (and often stalking) Jake. However, they occasionally switch roles.
Matt and Dusty from... well, Matt N Dusty, strongly invoke this whenever they talk to each other. Even by themselves, Dusty is a Jerkass to everyone and Matt occasionally gives off some passive aggressive vibes.
The Wisenheimer's Podcast between Yotam Perel (Lazymuffin) and Max Gilardi (hotdiggedydemon) thrives on this trope.
Voldemort and Quirrel from A Very Potter Musical. Harry and Ron also tend to act this way toward Hermione, but Ron, of course, is in love with her and Harry considers her to be like a sister. Ron also fits with his little sister, Ginny. To Draco:
She may be a pain in the ass, okay? But she's my pain in the ass.
Trixie and Jack of Black Jack Justice fit the bill. Not an episode goes by where the two PI's don't bicker and threaten each other at a pace that would make the Gilmore Girls jealous. They even have some pat, oft-repeated gibes for when they're tired ("You miss me?" "With every bullet so far" is pretty common). Police Lt Victor Sabien fits this bill with both of them. In fact, when an episode opens with Vic walking in and not insulting them, that's their first, best clue that he's truly upset.
For that matter, Jack and Freddie the Finger have a relationship of this sort, but a little softer and more gentle than the rest of the cast.
Lewis Brindley and Simon Lane from the Yogscast, especially in the Minecraft series where they're regularly hitting one another with diamond swords, pushing each other off blocks, and being generally snarky... And the rest of the time they're calling each other pal, helping each other through fear inducing challenges, and making Slash Fic jokes. Woe betide anyone who unites them against a common enemy.
In the Little Wood and So Totally Toby have a similar relationship. The two abuse and snark at one another constantly, with Martyn dishing out most of it, but they're good friends.
Speaking of Martyn Littlewood, he has this sort of relationship with both Strippin and Sparkles* as part of the "Dream Team". They all enjoy hanging around together, but Sparkles* spends half his time snarking at the others, while Strippin gets a lot of the flak.
Sips gets on well with Sjin, but the former spends most of his time outright abusing the latter. He also gets on well with Hat Films despite their collaborative videos and constant swearing at each other.
The group of Let's Players known as the Freelance Astronauts fall into this territory quite often in their videos - likely aided by the fact that they seem to have more or less grown up around each other, and have had years to get used to each of them treating the others this way.
Chuggaaconroy and ProtonJon in The Runaway Guys are consistently trying to kill one another [in game of course] and constantly make jokes at one another's expense, but it's clear that they do genuinely like each other.
Ian and Anthony of Smosh. They call each other horrible names, smack each other around, and sometimes just flat out kill each other. And yet they're still clearly best friends.
Frollo and Gaston from The Frollo Show. They're the best of friends and will fight to the death for one another, but can't help but dick each other over at every opportunity.
Pretty much everyone fom Achievement Hunter is this, notable examples are Jack and Geoff, and Michael and Gavin.
Josh Hadley and Scott Murray, hosts of Lost in the Static; on some shows, they seem close to breaking out into a fist fight. There were a few episodes at one point, in fact, where Scott took some time off, mainly to keep that from actually happening.
Coffee Talk and Sombra from Ask King Sombra. While Sombra may be largely self-centered, and their current relationship may hinging primarily on Coffee Talk blackmailing Sombra into behaving, he does care about Coffee Talk a little, as he immediately went off in search of her after he was revived, getting himself captured by Crystal Wolves in order to find her.
Mark and Cory of the Lets Play Modestly Proph Itic jump at any chance they have to insult, berate and screw each other over while recording, but off camera (off mic?) they are extremely close friends.
Ben Croshaw aka Yahtzee and his one-time bouncer, Gabriel Morton's relationship, or at how they're least depicted in their Let's Plays (or Lets Drown Out due to its podcast style). Gabriel's a recovering alcoholic—a source of much chortling from the oft-soused, self-medicating Yahtzee—who 'takes up space' at Yahtzee's bar and doesn't order any drinks, is prone to big pontifical statements, and seemingly dislikes any genre of game that doesn't involve "hit-y" things. Yahtzee has a competitive streak, compelling him to dissect everything Gabriel says and mock his shortcomings, such as his weight and investment in worthless history courses. It's apparently become so vitriolic that, in the beginning of 'Let's Drown Out Sims 3' video, they have to explain that they are best friends with each other and essentially told their viewers to go get friends in order to understand the subtlety of human interaction. Yahtzee also pointed out that if he openly insulted you, it means that he is comfortable enough with you to do so whereas if he's unnaturally polite, it meant he's gotten sick of you.
"It's because I'm comfortable enough to call you a fat, sweaty bitch that indicates my high esteem for you." "Yeah, y'know, and I call you vaguely-autistic shut-in nutbar."
If you did not know STAR__ by his 'Sniper Stomper' video, you may have known him from his famous trilogy(Ruiner of Fun, Jerma is Mad pt 2 and part 3) where he made his his best bud, Jerma985, mad as hell and sending him into the vulgar humorous rage while STAR_ effortlessly outplay him time and time again and it extends beyond those videos. It's still clear that these two are the best buds, seeing that they keep playing with each other.
The bears of Where The Bears Are are very close friends, though it's sometimes hard to tell given how Nelson and Reggie snipe at each other and how both belittle Wood.