Think about this : In That Wrestling Show, Red and Eric play an amicable wrestle battle at home at the end of this episode. Although Red tricks Eric in order to win the match and make him say that his dad is the king, Red actually gives him a hug which comes from his heart, not his conscience. It's a nice moment of heartwarming, even when you consider that Red usually despises Eric and can't express his feelings.
In fact, during first season, Red is actually nice to Eric. Even if he punishes him sometimes, he gives him advice in order to have the perfect job or evening with Donna or birthday, he gives him a survival kit for his week-end, allows him to organize a party, offers him 10 dollars if he works around the house and even admits he loves him, though he's drunk.
Don't forget the episode in which Grandma dies and Red laughs when Eric tells him that he believed it was his fault that Bernice died.
In the episode "The Keg", Kelso is sent to the store to buy a tap to open the beer keg that the gang found on the side of the road. He runs into a pair of jocks who harass him and break the tap, forcing Eric to have to steal Red's tap. Later, at the pool party(in the drained pool of an empty house), Eric confronts the jocks, telling them off and tearing up their money in front of them.
In one episode, Red finally sees Laurie's true nature upfront, and treats her with disappointment, leading to her becoming depressed. After initially revelling in the situation, Eric begins feeling sorry for her. The scenes between are beautifully heartwarming when compared to their interactions in almost every other episode.
There was also an episode where she comforted Eric after he became traumatized by seeing his parents have sex. She also briefly became a saint towards the end of her original actor's run, but reverted soon after with no explanation.
Really, any scene with those two actually getting along is heartwarming since they've been portrayed as antagonistic toward each other since the day Eric was born.
Anytime Laurie acts like a human being. You can count the instances on one hand, but they are brief and beautiful.
Kitty and Eric singing along to the radio in the car, after Eric joins her at work for a day. She's just lost a patient, and Eric tries to figure out how she does it. She just does.
Hyde and Leo are playing LIFE, which the latter greatly enjoys because of all the success he has in-game. When Hyde suggests getting back to work, Leo wants to continue playing because his life is better in the game - noting that his own kids split on him. When Hyde replies that his own mother abandoned him, the two bond as (a unconventional) family.
At the end of the Season 2 finale, when Hyde gets arrested for possession of pot that Jackie bought, so she wouldn't go to jail.
When Leo returns in Season 7, Eric takes him to back to the basement to see Hyde. Hyde is happy to see Leo again. The two talk for a few moments before Leo realizes who he's talking to.
Leo: Hey, wait a second. You're Hyde, man! (hugs Hyde)
"Hyde's Birthday", Red tells Hyde to go to his birthday party since he lives with Red and Red makes the rules, but Hyde replies that he plans on leaving since he's now 18.
Hyde: "My dad and my uncle and cousins were all on their own when they were this age." Red: "And where are they now?" Hyde: "Uuh... pumping gas, prison, prison, dead, prison." Red: "And the reason you're with us is so you don't end up like that. So, what's it gonna be Steven? Prison, death, or a birthday party?"
The final episode has a twofer, as Red reveals to Hyde that he'd kept every cent he'd paid the Formans as rent over the years, and was saving it for when he finally moved out on his own so that he would have some money to fall back on. This was actually a callback to Season 2 when Hyde first got a job and Red said he was going to put that money in a savings account for him (joking that he hadn't decided between that and blowing it all on booze) after Hyde voluntarily gave them his paycheck without them asking him. Hyde then decides to use that money to buy Red a season ticket for his beloved Green Bay Packers, something he had wanted for most of his life.
Any moment where Red and Eric actually bond. "Hunting" has an underplayed but strong one, Red asks Eric if he was serious when Eric said earlier Red has been yelling at him all his life, and tells Eric to say what he honestly thinks of Red. Eric replies that Red is unhappy with how his life turned out and is mean to Eric to make him grow up a stronger man who won't get pushed around like Red ended up being. Red smiles slightly and notes "maybe you'll turn out okay".
Red may be a hardass on his son. But mess with Eric in front of Red at your own peril. For instance, when a psychiatrist tells Red that the source of his stress is Eric:
Red: You think my problem is my own son?! My son is a fine young man!
Throughout the Season 8 premiere, Kitty records messages for Eric and tries to get Red to say he misses him. Red refuses and, in fact, tries to act like he's glad Eric is gone. In the end, though, Red admits that he genuinely misses having Eric around. When Red leaves the room, Kitty reveals she recorded him saying it.
When her dad goes to jail, Jackie seeks comfort from Hyde—who unsurprisingly is incapable of being sensitive. In the end, Hyde shaves off his beard (which Jackie hated) to make her happy.
The final flashback of "Class Picture". It shows the gang discussing the merits of I Dream Of Jeannie vs Bewitched over the years of their friendship. In the end, the entire gang is in the circle (one of the few times this happened on the show) laughing and goofing off. For anyone who has fond memories of hanging out down the street with their friends in high school, this is guaranteed a smile.
In the same episode, we learn that when Fez first met the other guys he was being harassed by the football team, but Hyde tells him if they bother him again to just come find him.
Red explaining to Eric that for family members, you only say "I love you" when you're in trouble or you're just drunk. As he says, "Otherwise, it's a given."
In "Til the Next Goodbye," everyone has a moment where they say goodbye to Eric. Yep, even and especially Red.
Mixed with a Moment Of Funny when Red accidentally admits that he considers Fez to be part of the family.
"I'm miserable because I had to spend the day cooped up in the car with that mustard gas you call cologne! But mostly I'm miserable because that's how we do it in this family!"
As an overall theme of the series, Kitty acting as a surrogate mother for Eric's friends, who all came from abusive or neglectful families. This is hilariously lampshaded by Red after Kitty offers to take Jackie in when her father is arrested and her mother hasn't come home:
Red: Kitty, every time we have an empty room, you want to fill it up with a stray child. You're like the Old Lady who Lived in a Shoe.
Kitty: Did you just call me old?
For as grumpy as he is about taking in Eric's friends, he actually does want to help but he's being realistic about how much it would cost and the Formans don't have a lot of money.
Hyde gets one as well for sneaking Jackie into the basement every night, not to have sex but because he doesn't want her in her house alone.
Doubles as a Crowning Moment of Funny, but when Jackie tells Eric that Kelso was also bad at sex during their first time in an effort to make him feel better, Eric admits it actually did help and thanks her for it.
In a more sincere moment, after Jackie started living with Donna's family after her dad had been arrested, Jackie had been acting like an insufferable creep and reading Donna's diary. Then she revealed to Eric and Donna that she had paid for Eric's engagement ring to Donna to make up for her behavior after Eric was trying to figure out how the debt was taken care of. From then on, Jackie and Donna end up becoming much closer as friends and even Eric seems to get along with her better.
Jackie did keep making remarks to the effect that Donna shouldn't marry Eric or have be with him, but as soon as she realized Donna was seriously wondering if she was making a mistake marrying Eric, Jackie told her that they were meant to be together.
In Season 3, when Hyde finds his father and decides to try living with him. He tells Red, who's about to tell Hyde not to loan his dad any money. Red doesn't say anything about the money, but his expression is a mix of anger, confusion, resignation, and worry, and then he says "You don't expect a hug, do you?" They hug anyway, and it's a very sweet moment between the two hardest hardasses on the show.
A little later, Red gives Hyde's dad (Bud) a "The Reason You Suck" Speech, telling Bud that Hyde doesn't need a friend, he needs "someone to ride his ass." Bud then turns around and starts acting like an adult for the first time.
In Season 3, Donna wins a pair of tickets to a Led Zeppelin concert. Eric has to work, and the rest of the gang spends the episode bickering about who should get the remaining ticket. Donna then gives the ticket to Fez and the girl he likes.
In the episode, "It's a Wonderful Life", Eric wishes that he and Donna had never gotten together. His guardian angel shows up and takes him further and further into the future of an alternate timeline to show him how badly it would suck. Eric remains unconvinced, even after getting a dressing down from his alternate future self, who deeply regrets never having made a move. Finally, at episode's end, the angel claims that he's given up on trying to change Eric's mind and is going to erase the relationship and take away the pain that came with it— but then shows Eric a montage of other things that are going to be taken away as well, the happy memories Eric has of being with Donna. This is what finally convinces Eric that he'd rather have loved and lost after all.
Hyde spent the night pulling fire alarms so Donna wouldn't have sex with Casey. Eric makes this a Crowning Moment of Funny when Hyde keeps insisting it wasn't for him and only because he wanted to do something illegal.
Eric: All I can hear is, "I love you, I love you, I love you."
When Eric is dealing with the fallout of breaking up with Donna, at first Red appears to dismiss it and force Eric to work and do chores. As the episode progresses Red sees the pain that Eric is going through. In a moment of true understanding Red tells Eric he can be as lazy as he wants and take time off work in order to cope with the breakup. This being tremendous since Red often takes a hard stance on any kind of laziness on Eric's part.
When Fez meets Nina's parents, they forbid the relationship because he's not white. Later on Kelso not only comforts him but when Nina comes around Kelso immediately jumps up and yells at her in Fez's defence. Fortunately, Nina agrees that her parents are racist and Fez forgives her immediately after learning she wants to sleep with him on her parents' bed.
In the episode "Grandma's Dead", Eric picks a fight with a guy in a bar, who knocks him out cold. The guy asks if Hyde, Kelso and Fez want to try anything Hyde's response is "Well, there's three of us, so..." and he and Kelso jump on the guy. This is weirdly heartwarming, seeing how they're usually so fickle.
A blink-and-you'll-miss-it moment, but during Season 7's "Let's Spend the Night Together," when Hyde meets his real father (played by Tim Reid). Hyde's father turns out to be well-to-do, and accuses Hyde of wanting money from him. Hyde leaves, and Red comes to Steven's defense. It shows that Red thinks of Steven as a son.
You're supposed to look at me, and know I raised fine young men!
In Season 1, Red and Kitty spend an evening having dinner with Bob and Midge and are perplexed by their outlandish behavior (which is a red flag to Bob and Midge's eventual divorce). After the couple leave, they discuss how bizarre their behavior is, uncertain how it'll affect their marriage.
Red: Now they're into every fad there is. Things change, Kitty. Kitty: Well, we don't. Red:(pauses, considering it) Well, we don't have to. (puts arm around Kitty, smiling) We're classic. (They kiss)
In the episode "Career Day," we see a bunch of heartwarming moments. Red ends up bonding with the paternally neglected Jackie over mechanics, Eric has a newfound respect for the work his mother does at the hospital, Donna realizes how far her father's willing to go so that she can go to a good school and have a better job than he does, and even Hyde has a moment with his mother after Red advises him to go back and talk to her after they have a fight.
Fez spends most of the episode "That '70s Musical" thinking his friends don't care about him; they forget to tell him about a party, and are apparent no-shows for his musical performance. They show up at the last minute, revealing they were delayed because they stopped to TP the house of a teacher he hates.
In "Fez Gets the Girl," Laurie is struggling through cosmetology school and Kitty's determination to keep her from dropping out is one of the few times we see them truly bond as mother and daughter.
In season 3 Hyde is the only person to remember Kitty's birthday and have a gift for her even though he's no longer living with the Foreman's at this point. It shows how much he cares about and appreciates Kitty, who's basically the only real mother he's ever had.
When Midge leaves Bob and Donna, Hyde talks to her about her brief relapse into intimacy with Eric. When she says she would have done it with anyone, Hyde jokes that hashed could have come found him, but then immediately tells her he's kidding, puts his arm around her and tells her he's sorry about her mom leaving.
It makes sense considering Hyde knows what it's like to have a parent abandon you(several times in his case) and, outside of Eric, Donna is probably his closest friend and vice versa.
In season 5 after Tommy Chong temporarily leaves the show, Hyde and most of the gang try to track down Leo since Hyde hasn't seen him in awhile. Hyde is adamant that Leo wouldn't go away without saying goodbye, and eventually they find Leo's cousin Eli who reveals Leo did leave town but he left Hyde a note saying why he was leaving and telling Hyde he's a good kid. Hyde momentarily loses his cool demeanor and Jackie remarks that he really does love that "old dirty little hippie". Keep in mind Leo was(in his own way) a father like figure to Hyde, and the only parental figure besides Red and Kitty that never ditched him.
The next scene has Hyde, Kelso, Fez and Jackie reminisce about Leo in the circle.
Meta heartwarming: Leo left the show because Tommy Chong had to serve a prison sentence tied to his glass pipe business. Chong was worried he would be let go from the show, but the producers assured him the fact that he was a huge stoner was why they hired him to play Leo in the first place. The instant his prison sentence was served, they didn't hesitate to bring him back on the show.
Jackie's relationship with Red. Out of Eric's circle, she is probably the only person who genuinely loves him, seeing him as a father figure. Red on the other hand, while often finding her annoying, seems to have a soft spot for her.
They first bonded in "Career Day" when the two are fixing the Vista Cruiser, with Red even admits that he finds Jackie likeable.
There are several occasions Jackie hugs Red for comfort, much to Red's discomfort.
During the seventh season finale, thinking that she leaving for Chicago and not be returning, Jackie calls Eric and tells him to pass the phone to his father so she can tell him that she loves him.
In "Going Mobile" Both Brook's Mother and Kelso are fighting over where Brook is basically going to raise her and Kelso's child. Kelso is trying his best to always be with her and his kid, but Brook's Mother brings up the point that she loves her daughter and is willing to offer everything to her so she could raise the child, while Kelso is off to the Police Academy for 6 months, she is just asking Kelso to do what's right for not only Brook, but for their child. Kelso, obviously looking hurt but understanding, tells Brook to have the Baby in Chicago with her Mom by her side, knowing that she's better off with someone who can be their 24/7 than him at the moment. Brook's Mother can't help but admit some respect for Kelso.
As a meta example, the marriage between Ashton Kutcher and Mila Kunis. It makes those times when Kelso was claiming he and Jackie were meant to be together a Heartwarming in Hindsight.