Avatar: The Last Airbender: Zuko and Mai's kiss at the end of "The Beach," an episode where they didn't seem to be having very much fun together, got into a big fight, and broke up briefly. At the end, Mai puts it best when she says "I know one thing I care about. I care about you."
In the episode "Harlequinade", the Joker finally manages to push Harley Quinn over the edge, prompting her to point a gun at him. The Joker taunts her that she will never have the guts to actually shoot him, but though shaking in fear and anger she actually pulls the trigger... only to reveal to the both of them that the gun was a "Bang!" Flag Gun. In response, the Joker scowls at her and her determination quickly melts away and she looks nervously back at him, but his scowl turns into a sincere smile as he tells her: "Baby, you're the greatest!" And the two embrace.
In "Mad Love", the Joker, in quite a grumpy mood, pushes Harley Quinn off a building, injuring her deeply. She finally comes to see that he never cared for her... Until she sees roses and a get well card from him. Awwwww(ful).
There's also the episode, "You Scratch My Back", where Batgirl chastises Nightwing (aka Dick Grayson) for his aloof behavior as well as the fact he's partnered with Catwoman. They eventually show their feelings to each other by the end of this episode.
In an episode of Chowder, Mung and Truffles get into an argument that escalates in vitriol and volume; it ends in a prompt make-out session. They part with "GET AWAY FROM ME."
Dan Vs.: Even though Dan typically treats Chris poorly, he has been shown to care about him and has helped him out a few times, if seemingly grudgingly. This was best shown in episode "The Boss". In that episode, Dan finds a successful career as a temp, calling the company's debtors and late-fee holders and persuading them to pay their debts. Dan is forced to fire Chris, and when he learns his boss was really a demon, he had no problem with this; he's even happy to be going into big time evil. However, when his boss wants him to kill Chris, he turns on her to protect him without any second thoughts, showing that Dan truly does care for Chris in the end.
Jake and Helen in Daria, despite all of their squabbling and conflicting schedules, still seem to really care about each other. In one episode, Helen tells Daria about their first anniversary, Jake made her a poorly constructed candle that was supposed to be a Hobbit, which he then accidentally dropped into the hot tub they were sitting in, causing it to melt. Helen then noted to Daria that instead of being disappointed with her gift, she realized "a lot of time and love went into that silly lump of wax." The end of the episode reveals that she still kept it after all those years to remind herself why she married him.
This is Eddy's relationship with his friends. In later seasons he treats them quite badly, but some episodes (and especially the movie) show that he genuinely cares about them.
Don't expect her to openly show it, but there are at least two moments ("Honour Thy Ed" and the end of the movie) where it's confirmed Sarah does love Ed deep down.
In one episode of Family Guy, Brian is replaced by "New Brian," and Stewie tries to convince him to come back.
Brian: You always said I was a douche. Stewie: Yeah, but you're my douche.
Father of the Pride: Despite fighting most of the time, Sierra and Hunter are seen actually getting along from time to time. For instance, they are seen playing a video game together in "The Siegfried and Roy Fantasy Experience Movie."
In Futurama episode "Zapp Dingbat", Leela is utterly disgusted when her mother starts a relationship with Zapp Brannigan and tries to break them up by proving that Zapp is a lecherous creep. However, he is in love with Munda, and resists Leela's lingerie-clad attempt to seduce him so he can propose. Before the wedding, he manages to offend Munda by being his usual General Failure self.
The first glimpses we get from the Fry family, they all seemed like selfish people who Fry was glad to be rid of. But all of them ultimately showed concern for Fry, and were upset when he disappeared.
Every so often the Planet Express crew will show that they do indeed like Zoidberg more than they seem to.
In the Garfield Specials, this is how Garfield and Odie are depicted. Even though Garfield repeatedly berates Odie and Odie does not seem to notice, there are moments in the specials that show they actually care about each other. Notably:
In "Here Comes Garfield", Garfield helps Odie escape from the big sleep in the dog pound.
In "Garfield's Halloween Adventure", after Odie saves him from drowning in the river, Garfield, who was initially going to keep both his and Odie's bags of candy for himself, shows his gratitude by giving Odie his half of the candy.
In "A Garfield Christmas Special", Odie gives Garfield a homemade backscratcher, which Garfield enjoys, and hugs Odie.
In the "Garfield" segment of Garfield: His 9 Lives, Odie saves Garfield from getting hit by a truck, and Garfield is eternally grateful. However, this is Subverted, since it is shown that years later, Garfield tells his grandchildren the inverse happened.
In the epilogue of the same special, God gives Garfield the chance to live all of his nine lives again. God then asks if Odie is also a cat, and Garfield claims he is. (Odie even "meows" to keep up the charade.)
Glitch Techs: Miko and her family tend to act rather uncaring, but any episode that focuses on one of them along with Miko will show that at the end of they they are a very loving family.
In Hey Arnold!, Helga frequently clashes with her parents and sister, but many episodes show that they really do care about each other ("Olga Comes Home", "Quantity Time" and "Road Trip" are a few examples.)
Jamie-O is usually a Big Brother Bully to Gerald, but there are a couple of episodes that show he does care about his little brother deep down.
John Stewart and Shayera Hol in "Comfort and Joy" and "Wild Cards".
Flash and Hawkgirl share a similar heartwarming scene in the finale. He was very vocal in his defense over why Hawkgirl shouldn't be kicked out of the group and before she left on her own, he stopped her so he could hug her. Reciprocated in the Season Fauxnale of Justice League Unlimited, 'Divided we Fall'. When Flash proceeds to trash the combined Luthor/Brainiac entities by punching repeatedly him at superluminal speed, and literally skinning Brainiac from Luthor's body at superspeed is called into the very source of his powers, with no way to return back Shayera seems unable to accept his apparent fate. She then instigates an human chain inside the Speed Force, literally begging Wally to "take her hand" and return to the real world. When she finally gets her friend back, she tenderly caresses and hugs him, with her on-and-off boyfriend John Stewart joining in as a cheesy, happy family glad to have gotten their wayward kid back.
Batman has several moments with the other Leaguers that show the heart of gold underneath the cowl, especially with his Foil, Superman; case in point, Supes bear-hugs Bats at the end of "Savage Time." He also protects them from personal threats (even though these people have superpowers and could break him in two), whether it's helping Flash deal with his Rogues Gallery or checking out Shayera's new beau like an Overprotective Dad. He's not a bat, he's just a big ole teddy bear!
Percy and Anastasia. They routinely fight with and cheat on each other, but are still in love (or at least lust). They also get extremely jealous when the other cheats — Anastasia gets pissed off when Percy hires prostitutes, while Percy will cheerfully attempt to kill anyone who dates Anastasia.
Percy and Anastasia supposedly keep Kevin around for the money they would get for having a dependent. A flashback reveals that they really do love him, and Anastasia breaks down in tears when they had to give up Kevin's twin brother for adoption.
Les Sisters: Marine and Wendy, the titular sisters, enjoy annoying each other and fight a lot, but they don't like it when other people mess with the other one and they are horrified when their parents suggest separating them to stop them from fighting and causing chaos.
There's a non-romantic example in the season two finale.
Toki Wartooth: Nathans, the real reason you tells me this is that you cares abouts me.
Once in a blue moon someone will say something about how they do consider the other band members (or the Manager) their friends. To name a few:
Nathan calling the band is "stupid, dumb, fucked up dysfunctional family" in Fatherklok. He also insists in "Dethzazz" that the rest of the band has to help Toki recover from his punishment coma despite the fact that the band wouldn't suffer at all musically from his absence.
Pickles' line about calling the band his family in Rehabklok.
Charles telling the band that they're all important to him in Doublebookedklok.
Nathan apologizing to Pickles despite the fact that doing so literally causes him to vomit blood and cringe in pain.
Averted in Moral Orel. After all the crap they've put each other through, Clay and Bloberta genuinely hate one another, and their own children. The only Aw Look They Really Do Love Each Other moment even vaguely suggested in the show is the fact that Clay tears up for a split-second when talking about the mistakes he's made during a drunken rant. The other residents of Moralton fare little better, though there are enough Pet the Dog moments to keep it from being an irredeemable Crapsack World.
Rarity and Applejack have very different personalities, and when the series started, couldn't stand one another. Even after they got over their initial dislike of one another, they were still very likely to snark or needle one another. Every so often, however, they'll stay or do something to show how much they care.
Applejack: But good things are better when they're a Rarity. [winks] Rarity: Ooooh!
Rarity also has this relationship with her pet cat Opalescence. Their relationship is rocky at best with Opal usually swatting at her owner whenever she tries to come close. However, Opal is shown to care for Rarity as she worries about her in issue #23 of the comic and reminds her to make Twilight's birthday dress in "Sweet and Elite".
Also, Rainbow Dash and Fluttershy. In the beginning, Dash seemingly couldn't stand being around Fluttershy, despite them apparently being close friends since childhood. But she shows time and time again that they do care for each other, and later seasons do make that years-old friendship less of an informed trait.
Phineas and Ferb: Buford and Baljeet have a very interesting relationship. Although Buford is "supposed" to bully the smaller nerd, they have times when it's obvious that they actually do care about each other. In "Bully Bromance Breakup" Buford states that "[Sometimes] you just want to bully someone you love," and Baljeet discovers that accomplishing a great feat is not as satisfying when he's not sharing it with his best friend. They also sing a song entitled "Frienemies" in the episode "Lotsa Latkes." In "Mission Marvel," Buford manages to calm down Hulkjeet by telling him "I worry about you, you know. Because...you're my best friend." Of course, then he makes Baljeet angry again by demonstrating the proper way to lift someone by the front of their shirt...
Hulkjeet:DO NOT YELL AT BALJEET LIKE THAT!!! *throws Buford and runs off in a rage* Buford:*lands in Ultra-Soft Bedding Warehaüs* Okay, the throwin' was good! But when you grabbed my shirt, you didn't twist!! I swear, it's like in one ear and right out de other! Oh, oh! Baljeet, wait up!
The Scotsman and his wife from Samurai Jack. He's head over heels for her the entire episode, but she spends the entire episode hollering and insulting him. Then finally at the end she admits "it was sweet of him to rescue her", and makes a complete change into a friendly and kindhearted woman.
In "The War of the Simpsons", when Marge and Homer go to couples counseling, another couple is shown bickering, and throwing mean, petty insults at eachother. Then the reverend asks them to look into each others' eyes...
In "Mother Simpson", Homer's long lost mother returns and neither she nor Abe is happy to see the other. Yet when the FBI raided the Simpson house to arrest her, Abe's immediate response is to provide a distraction so Homer can get her out of there. Though Abe admits to not being totally certain if it was a distraction or just senility.
Abe: A little from column A, a little from column b.
"Burns Baby Burns: Burns meets is long lost son, Larry, but finds him to be a boorish oaf and gradually wants nothing to do with him. Homer and Larry attempt to invoke this reaction into Burns with an ill-thought out kidnapping scheme, but Burns doesn't show concern, only anger at being robbed. After Larry comes clean, Burns admits while he glad to know Larry, he wants nothing to do with him afterwards.
The Smith-Sanchez Family do have their moments that show they care for another despite toxic dysfunction. But as those moments unfortunately are moments, they don't last and their toxic dysfunction remains an ongoing problem that none of them want to work to resolve. Even if at the end of Season 3, the family has returned together, it's more or less as a self-conscious facade and charade, i.e., rather than true appreciation and growth for one another.
Thought out the first two seasons Beth and Jerry show moments were they care for each other despite toxic dysfunction marriage. But those moments unfortunately are just moments, they don't last and their toxic dysfunction remains an ongoing problem that they don't work to resolve. In Season 3 when Jerry put his foot down and make her choose between him and Rick, she chose Rick.
Jerry and Beth do not have a good marriage, and are sometimes unsure if they're even in love, but one always has the other's back when push comes to shove.
The titular characters as well. Rick, despite his abrasive behavior, always wants what's best (well, at least what he thinks is best) for his grandchildren and isn't above having fun with them once in a while. He's abusive as hell to Morty and typically treats him as a means to an end, but there's little doubt he does genuinely care about him.
In ''Get Schwifty", Jerry outright says he's sick of pretending they only stay together for their kids. He married Beth because he loves her and wants her to know that.
"Rixty Minutes" shows an alternate timeline where Summer was aborted. Jerry becomes a movie star, and Beth is rich enough to sit at home all day. This leads to a lot of hurt feelings between "our" Jerry, Beth, and Summer. It turns out that in the alternate universe, Jerry's miserable and Beth is a Crazy Parrot Lady. Jerry has a meltdown and drives all the way to her house on a Rascal mobility scooter in nothing but his underwear, police and media on hot pursuit, to confess his love for her. This leads to "our" dimension's Jerry, Beth and Summer to patch things up.
In "The Wedding Squanchers" The Smith family become fugitives after Rick is discovered to be wanted for terrorism by the galactic federation. Jerry suggests that they turn Rick in so they can have a normal life but the rest of the family refuses because they love Rick(for the most part). Rick has a revelation and turns himself in anyways. Though later subverted when it turns out he got caught on purpose to not only topple the government but push Jerry and Beth to separate, letting him in his own words "become the de-facto patriarch of the family and the universe.
"The Ricklantis Mixup shows a Rick who is "more into working with wood than science," and creates a jewelry box (complete with a cartoon horse on top) for his daughter's birthday, truly demonstrating his love for Beth. This is then ruthlessly invoked as the scene pans out to reveal that this Rick is kept a prisoner, with this memory being played on an infinite loop just so the "happy" chemical his brain secretes can be extracted. This is done by other Ricks, to add flavor to a wafer.
Rick is reluctant to see Jerry killed, being genuinely horrified along with the rest of the family when Jerry was almost shot to death in "Interdimensional Cable II: Tempting Fate", keeping him alive despite Jerry betraying him in "The Whirly Dirly Conspiracy", killing his ex-girlfriend's jealous boyfriend in "The ABCs of Beth", and not going through with killing him in "The Rickchurian Mortydate".
Star Trek: Lower Decks: In "Moist Vessel", Ensign Mariner and Captain Freeman briefly put aside their long-standing animosity and hug each other after they save the crews of the Cerritos and the Merced. When they realize that they're in an embrace, they quickly let go and pretend like nothing happened.