Louise crying because Bob and Gene won't hang out with her anymore. Made even more heartwarming because of her usualpersonality.
Also Bob and Gene's interaction in this episode, bonding over a series of films.
Gene and Louise getting back at Tammy, the girl who was blackmailing Tina doubles as this and Crowning Moment of Funny. Includes this memorable line from Gene, who sums up exactly what fans and critics love about this show:
Gene: We're Belchers, from the womb to the tomb!
Any time Bob does something crazy for his children's sake (and for his wife, as seen is the dinner theater episode). It happens a LOT for Tina in the first half of Season 1. Fighting Jairo? Check. Shaving off his mustache for her? Check. Bob may think his family is crazy (and they are), but he'll do anything for them, and it's both hilarious and sweet. Tina put it well.
Tina: Jimmy Junior isn't gonna make this party perfect. You already have.
Speaking of "Sheesh! Cab, Bob?", the characterization of the transvestite hookers in that episode is actually kind of sweet. A lesser show would've treated them as walking punchlines the whole show (and indeed, their seedy lifestyles do contribute to some of the episode's humor) but never once does Bob - or anyone - dehumanize them. In fact, not only did they briefly become Bob's drinking buddies and may have gotten him to try crack, they wound up giving Tina a heartfelt pep talk near the end of the episode.
There's something sweet about Gene's reasoning for why he couldn't remember the name of the restaurant when given the opportunity to do free advertising. As he describes it: "You're my dad, I think of it as Dad's Burgers." That's... actually really sincere for a child Gene's age.
In the 3rd season Christmas Episode, when the kids willingly give up the hard-earned money earmarked for their presents to buy the mannequin from the sex shop owner for their deranged house guest, who is in love with it. This show makes that heartwarming.
"Lindapendent Woman": Linda gets a new job at a supermarket. Not only is Bob miserable without her, but between that and the fact that the restaurant's finances collapse without her to sort out the bills, he still gets over his initial bitterness and tells her that if the new job makes her happier he's fine with her keeping it.
Gene's friendship with the high tech toilet from "OT, the Outside Toilet".
"Bob Fires the Kids". Not sure what's better, that Bob fires them because he's afraid their childhood working will be as bad as his was, or that the kids are genuinely disgruntled at not being allowed to hang around the restaurant all day.
The blink-and-you-miss-it moment in the beginning of the episode, when Louise actually feels sad for Bob upon seeing his box of makeshift toys from his childhood.
After Tina meets Josh from the supermarket, it almost seems like they'll never see each other again...until she comes across him walking home. It's nice to see a person who doesn't alienate Tina and Josh is genuinely interested in her.
"Carpe Museum," when Louise is snarking with Bob and alludes to herself one day running the restaurant. Bob lights right up realizing that Louise, on some level, actually looks up to him, and Louise's embarrassed denial is just plain cute.
Louise hugging her father at the very end (along with Rudy) adds to the sweetness.
Bob: Hey, I'm glad we ditched. That was fun.
Louise: Me, too. Let's do it again sometime. Like, maybe when you're old and senile, I'll close the restaurant and come spring you out from the nursing home.
Louise: Sorry, I didn't want to do it, but Gene and Tina put you in a nursing home. And not one of the nice ones either.
Bob: No, you said you'd be running the restaurant.
Louise: Oh, no, I was just saying...
Bob: You're taking over the family business?
Louise: (scoffs) Yeah, right.
Bob: Ha! Admit it, you look up to me.
Louise: No! You are ruining our perfect day right now!
Bob: Oh, my god, am I your hero?
Louise: (groan) Sick!
(at the end of the episode)
Bob: So, when you run the restaurant, will you call it Louise's Burgers?
Louise: I don't know. Maybe. (hugs Bob) Daddy.
"Boyz 4 Now". Louise and Tina have a bonding moment when Louise has her first crush. Louise ends up saying that she thinks Tina is a strong woman because although Tina has crushes all the time (which Louise hates), that Tina can handle herself without freaking out is something she admires.
The Reveal of who was dunking Bob's turkey's in the toilet in "Turkey in a Can". It was an allergy medicine induced sleepwalking in Bob, who was using the Turkey to represent his memories of potty training Tina, representing his subconscious fear of her growing up. Not only is the flashback of Bob helping a two year old Tina sit on the potty heartwarming enough inn itself, but it's then topped by Tina assuring Bob she still needs him and Bob allowing her to sit at the grown-up table.
The first episode has Linda and the kids reassuring Bob that despite all his failures, the fact that he's pursuing his dream of a burger shop makes him better than Hugo who never had a dream at all.
A blink-and-you-miss-it moment, but in Seaplane! as Linda has to land the seaplane by faking a crash the way her instructor did, Gene freaks, grabs his sisters' hands and the three hold on to each other.
In "Presto Tina-o", Jimmy Jr. and Tina making up after their big fight and winning the award for best on-stage chemistry.
In all three of the kids' stories in "The Frond Files," Gene, Tina and Louise always stick together when there's danger. For all the jokes and snark, those kids are some of the most close-knit siblings on TV.
In a shockingly selfless act, Louise traps herself with the bratty, incredibly annoying Tammy for several hours so that Tina can steal the spotlight at Tammy's party. She also pretty much ends up taking Tammy hostage at one point, making her promise to invite Tina to all her future parties or be trapped forever.
In "It Snakes a Village," Linda is initially furious with Bob for encouraging her parents to attend a swingers' potluck, but changes her mind when she sees them kissing each other for the first time in twenty years.
Linda: Huh. I guess if you love something, you let it go swing.
In the same episode, an elderly woman sends the kids in search of a giant python that ate her beloved chihuahua. In the end they find the dog, safe and sound, and reunite him with his owner, only to have him immediately run off again. Tina consoles the woman by telling her that the dog seemed really happy living in the woods. The last scene of the episode shows the dog and the giant python snuggled together inside a hollow log.
"The Kids Rob A Train" gives us the return of Regular-Sized Rudy, with Louise taking him surprisingly seriously. She puts a lot of stock in his train map, pays close attention to the plan and chides Gene and Tina for "embarrassing her", and assumes Rudy is going to take the chocolate and leave her because that's what she would do. She also shoves him away from the chocolate when she learns he's allergic and completely freaks out when he pretends to be choking. There's definitely still some ribbing involved, but it seems like after the events of "Carpe Museum" she sees him as a real accomplice, which coming from Louise is a big compliment.
On that note, the fact that Rudy helped the Belcher kids with a ridiculously complicated and dangerous espionage mission on a moving train to steal a huge bag of chocolate which he knew he couldn't even eat. The entire thing was so they could eat chocolate and be happy while stuck in the Juice Caboose. That's actually very, very sweet.
In a similar vein to the above, "Slumber Party" ends with Louise actually making friends with Jessica, based on respect for her scheming, evidence disposal and pillow-fighting skills. The end credits show a fashion show with all the characters from the episode parading by, ending with Louise and Jessica chasing each other with pillows and laughing.
"Uncle Teddy" shows that Teddy is now basically an extended part of the family, as protective and caring for the kids as their parents.
"The Equestranauts" shows us once again how far Bob is willing to go when someone has done something wrong to one of his kids, in this case helping Tina get back her prized Equestranauts toy after it gets swindled from her at a convention.
There's also Tina's relationship with the group of "Equesticles"note A knock on the "brony" fandom she meets at the convention. While their leader Bronconius only acts like her friend to steal her toy and puts everyone else down, the others are genuinely friendly to her and each other, which quickly makes her feel at ease after being put off somewhat by the idea of grown men who avidly enjoy a little girl's show. This comes into play later on when Tina convinces them to turn against Bronconius for manipulating them through something they love to fulfill his own, twisted desires.