In the extended pilot, Michael is upset that George Sr. gave the promotion to Lucille instead of him...until he finds out that it was to keep the rest of the family out of jail. It was a hilariously misguided plan based on a faulty premise, but his intentions were noble.
Michael Bluth gets a publicist to help improve the family's image. He starts dating her but then breaks it off because he is worried about it affecting George Michael. The publicist confronts George Michael and asks him why he is trying to keep his dad from being happy. Michael Bluth (without knowing this) takes the publicist out to dinner to try and patch it up where Michael's mother and sister confront her to attack her (she had written an unflattering article about them). Michael tries to stops them, however during the ensuing conversation the publicist mentions what she said to his son. Michael's response? "You said that?! You said that to my son!?" He steps back. "You're on your own." And his sister and mother proceed to beat the crap out of her.
Another great one is when George Bluth Sr. find out that his wife is in love with his twin brother Oscar and that Michael can get out of legal trouble if he turns George Bluth Sr. in. He proceeds to tell Michael to make a deal for himself as he (George) has no more love in his life. The episode ends with George waiting in the attic for the police to show up. Michael comes up and tells him that he did not turn him in, and he is sorry that he feels he has no love in his life. George Bluth Sr. says "I, I don't feel that way anymore." He then hugs Michael "Thanks Mikey, it's been a long time since someone stuck up for me," and kisses Michael on the forehead.
For this troper it was when George Sr. breaks back into prison to prevent his wife from sleeping with the warden, and tells her that however lousy their marriage is he doesn't want it to be thrown away, ending it with "No one is breaking this family apart, no one."
A touching moment occurs when Michael and GOB, both attempting to teach George Sr. a lesson, pretend to fight. During the tussle, Michael is seemingly thrown over the penthouse's balcony, to which George Sr. responds with a horrified "NO!". Of course, Michael is revealed to be safe, but the moment before this shows that for all his corruption and greed, George Sr. is at his core a father who deeply loves his son.
A sort of strange one occurs in Motherboy when Buster and Michael crash the Motherboy dinner-dance to rescue George Michael from Lucille, knowing how humiliating Motherboy is. Buster also crashes the party because he's angry at Lucille for basically rejecting him because of his hook prosthetic. At the end of all the mayhem they cause, he asks his mother if she'd still dance with him, even with his hook. She puts her scarf around his neck, tells him that he can be Captain Hook and she Peter Pan, and they dance together.
The end of "Storming the Castle" is a little bittersweet for Michael, but Lindsay does show him some genuine sympathy, and George Michael cuts him some slack for taking the chair from work. The look on Gob's face when he sees that Marta is the assistant Michael got for the show is also very heartwarming, as is his sheer happiness when he approaches his mother afterward. His happiness then inspires Lucille to accept Buster's relationship with Lucille 2 and have a sincerely friendly interaction with the latter. And, after years of stealing from Michael, Gob finally gives something back.
Heartwarming and heartbreaking all at once: "You gotta put family first. That's the stupid thing I believe."
You know it's true... Everything that I do... I do it for you.
When you think about it, the whole basis for the show. Michael gives up his chance to get away from his crazy relatives and finally be happy, all because his son was lonely and needed a family.
George Bluth Sr. occasionally shows that, much as he failed raising his own children, he wants his grandchildren have a better life, as his reaction to GOB sending George Michael to steal documents shows.
After Michael is freaking out about the botched business deal he made, Lucille, in a rare moment, comforts him:
Lucille: Michael, you made a mistake. You're a human being. But you're so forgiving to everyone else in this family. Try being forgiving to yourself.
Why are you squeezing me with your body?
When it is revealed that Michael kept many of George Michael's childhood drawings and crafts in a folder in his drawer at work.
"[George Michael] always knew his father loved him. Now he was holding the proof in his hands."
The revelation that George Sr. paid off all the other inmates so they wouldn't sexually harass Lindsay when she came to visit him in prison.
When George Michael finally admits his love for Maeby to his dad, and Michael, instead of being offended and judgmental (like usual), understands his son's feelings and only objects to the relationship because it might screw up their familial bond, which would last longer than any fling would.
When Maeby realises she's become a successful film executive, the first thing she does is get a job for her Dad. Whatever her intentions, the immediateness of it is touching.
Lindsay helping Tobias get rid of his never-nude affliction, and subsequently proving that regardless of what she says - she does love him, and their marriage wasn't some sort of cosmic accident.
The end of Pier Pressure was also heartwarming, when Maeby, after spending the day with Lucille and realizes how critical she was of Lindsay, tells her mother that she is glad to be Lindsay's daughter and gives her a piece of jewelry that Lucille always kept from her. Lindsay then hugs Maeby and this shows that difficult relationship aside, Maeby and Lindsay do love each other.
In the second season premiere, when the Literal Doctor led the family to believe that Tobias was dead, the whole family is shocked, even Lucille, Gob, and Maeby show genuine grief, proving that they did care for Tobias. Likewise, that are extremely angry and Dr. Wordsmith for misleading them.
Episode 11 with Gob and Tony Wonder admitting that they have feelings for each other (whether the feelings are of friendship or of love is not 100% clear) and just their whole bonding process, which started more as them trying to avenge each other for whatever reasons but actually grew into something fantastic.
Michael was frustrated that he specifically ordered his family not to sell their shares as soon as they were unfrozen (even though he hypocritically bought a new car with his share). He discovered that Buster was the only one who read the note and refrained from spending any of the money because he didn't wanted to hurt the family.
When Michael tells his father that a mysterious British man has threatened "someone stupid in our family", George immediately says he's going to change his plea to guilty, even though it would mean returning to jail. Michael assumes the threat was meant for Buster, but George suggests Gob could be the target, and actually seems worried - insulting as it it for Gob that his father openly thinks he's stupid, it's just about the only time in the entire series when George shows any sign of caring about his oldest son.
The narrator refers to Buster as "someone moderately intelligent", which is about as complimentary as he gets with the Bluths.
According to The Other Wiki on Michael's character profile: "Michael's wife Tracey died of ovarian cancer two years prior to the first season. Possibly, as a result of this, he is very close to his son, George Michael..." That alone is beautiful right there.