In "To Where andBack Again", the sixth-season finale of My Little Pony: Friendship Is Magic, a team of misfits assembles to do the world-saving typically done by the protagonists, who are indisposed. Although the group members are not all averse to teamwork, none of them are used to being team players, and at least one is actively antisocial. Of course, this just makes the group dynamics all the more interesting, and the eventual victory all the more fulfilling.
The Five-Man Band from Code Lyoko starts out like this, evolving into a True Companions as the series goes on. Though technically fueled by their Power of Friendship towards Aelita, in the beginning they don't really have much loyalty to each other, and it's kind of easy to get them to break up or lose at least one member.
In Young Justice, the villains Sportsmaster and Cheshire obviously can't stand each other from their first appearance together. Fridge Brilliance kicks in a few episodes later when it is confirmed that Sportsmaster is Cheshire's (verbally and emotionally abusive) father, who she ran away from home to escape.
This also occurs between Kid Flash and Artemis for a while after Artemis' arrival, since Wally saw her as usurping the position that should have been occupied by his friend Spee- sorry, Red Arrow. All of this ends when they enter a relationship in season 2.
In the BattleTech animated cartoon, the 1st Somerset Strikers don't exactly get along all the time.
Starscream and Megatron are stuck working together for good part of season 3. They clearly hate each other and don't even bother to hide their contempt for the arrangement.
Lugnut and Shockwave are united in one thing and one thing only; Undying Loyalty to Megatron. Otherwise they absolutely despise each other and spend most of their time fighting to prove whos the better underling, whilst an increasingly annoyed Megatron wants them to just shut up and do their jobs.
This happens occasionally on Kim Possible, notably in the episode "Go Team Go" when Shego teams up with Kim and her estranged family to defeat Aviarius.
Slade teamed up with the Teen Titans to save Raven and the world in the "The End" episode arc. Slade and the Titans still absolutely hated each other's guts, but managed to cooperate for some time. (Craziest part? Slade was a least trying to be polite about it, Robin was not.)
This happens a lot in Archer, the ISIS employees tend to get into petty fights on a daily basis. Whenever Archer and Lana are on mission together, Archer tends do stupid things that mess up their mission. Things get worse when the rest of ISIS take part in a mission, at least one of them will slip up, or were the cause of why their mission is compromised.
Happens frequently between Dudley Puppy and Kitty Katswell on T.U.F.F. Puppy; they are a dog and a cat, after all.
The Season 2 opener of Iron Man ends with Force Works dissolving as Scarlet Witch, Hawkeye, and Century decide to quit after Tony fakes his death and War Machine and the Julia Carpenter Spider-Woman deciding to stay. While Spider-Woman, Century, and Scarlet Witch don't hold anything against the others, War Machine and Hawkeye do have mutual contempt for the other side, with the latter making being an ass to Rhodey and Julia for staying with Tony and Rhodey likewise being hostile towards Clint and even making a snide remark about Wanda about their leaving after she and Clint return.
In Jack in the Scotsman's relationship starts out this way, with them (despite Jack's best efforts) getting into a prolonged fight almost immediately after meeting each other and only end of (reluctantly) working together, because a group of bounty hunter handcuffed them together. Though after they get themselves out of that predicament, they have grown to respect each other as warriors, with the Scotsman even becoming Jack's only real recurring ally for the first four seasons, with them still occasionally butting-heads, but more as a friendly rivalry, than genuine displeasure with the other.
There's also a villainous example with Josephine and Ezekiel Clench, a pair of formerly married bounty hunters, who reluctantly put their differences aside to capture Jack, but spend just as much time bickering with each other. They actually do manage to capture Jack, but Josephine lets her greed get the better of her and betrays her former husband, giving Jack the opportunity to free himself.
In the Rick and Morty episode "the Ricks must be Crazy," Rick and Morty encounter Zeep, an inhabitant of the micro-verse Rick created to power his car. When Rick demands to know why the micro-verse isn't generating electricity anymore, Zeep reveals that he created a mini-verse to power his world, where they discover that an inhabitant of the mini-verse intends to do the same thing in a teeny-verse he's just created. After being stranded for months inside the teeny-universe, Zeep and Rick spent that time arguing over who's smarter. When Morty shows up leading the Tree-People, he tells Zeep and Rick to work together and fix the machine that will transport them home, just as they are going to explain why they can't work with someone whose intelligence they consider inferior, Morty sics the Tree People on them. Sometime later, they fix the machine, they exit the teeny-verse, and their rivalry resumes.
In Castlevania (2017), Trevor's abrasive personality makes it difficult for anyone to co-operate with him. When he rescues Sypha from petrification in the castle dungeons and she stays with him to find the Sleeping Soldier, she still considers him to be rude and considers the merit of making him drink her urine. It's even worse when they join up with Alucard, who, being a Dhampyr, naturally has reservations about working with a Vampire Hunter like Trevor. With that said, though Alucard and Trevor frequently trade barbs and threats with one another, they still sometimes make one another laugh.