The end of the pilot where Virginia sings "Danny's Song" to Hope while Burt plays the guitar. Especially sweet when it flashes back to teenage Virginia and Burt doing the same thing to an infant Jimmy.
Considering how much they were against Jimmy keeping her (and still were in this scene) they manage to get over this to help comfort the baby.
Jimmy confessing to his parents why he wants to keep his baby, he sees her as a chance to finally do something worthwhile with his life. He knows he hasn't been motivated and wants to improve himself with his daughter being his motivation.
The ending of "Dream Hoarders". Jimmy is adamant that they can't continue with irresponsible behaviors like wasting money on lotto's and Virginia storing random (and dangerous) junk for a house they will never have. Jimmy has a point, but after talking with Sabrina he realizes his parents were always dreaming of something better, and relents on those actions.
As twisted as it is, the reason behind Burt's actions in "Happy Halloween". He loved the way it felt when Jimmy ran to him for comfort and was upset that these instances became fewer as Jimmy grew up so he started scaring the bejesus out Jimmy in order to be the hero in his son's eyes.
Jimmy: Even though I was a mistake, I'm a mistake my parents would gladly make again. And that is something you and I definitely have in common. I couldn't have planned how you came to me in a million years, but I always want you to know that you're the best thing that has ever happened to me.
Burt wants Jimmy to continue working with him instead of going to work at Howdy's, but also realizes that Hope needs medical insurance so he swallows his pride and takes a second job with a much-hated former boss so that he can continue working with his son while properly providing for his granddaughter.
The first season finale features flashbacks that show that Jimmy had become a bratty teen acting out towards his parents. But when he gets in trouble, the first person he runs to is his father and Burt immediately takes action to protect his son.
The revelation at the end of "Don't Vote for this Episode" that the Chances aren't abusing Maw-Maw's dementia for a free house. They actually proved themselves capable of living on their own, but when Maw-Maw started having problems, they swallowed their pride and moved back in to take care of her.
In addition, everyone yelling "Surprise!" every time Maw-Maw forgets it's her birthday party.
Maw-Maw: Oh my goodness! For me?
In "Sabrina Has Money", when Sabrina apologizes to all of her friends for lashing out at them due to insecurity issues, and Virgina returns the 2000 dollar gift toilet and 100 dollar lobster after getting carried away with fantasies about a rich life.
Burt "stealing" the perfect wedding for Virginia.
Burt's father calling Burt "a better man than me" for being able to deal with living a working-class life in order to support his own family.
The whole last 5 minutes of "Jimmy's Fake Girlfriend" with Jimmy writing a play for an improv group to show Sabrina how he's always loved her.
A minor one: In "Spanks Butt, No Spanks" Sabrina comes into the kitchen in the morning, the first thing she does is hug and kiss Hope, like a mommy would.
In "Poking Holes in the Story," Virginia laments that she's always wondered if Burt stayed with her for her or because of the baby, and if she held him back from something bigger in life, not knowing the Burt is listening. Burt admits that he poked a hole in the condom so that she would get pregnant because he was so in love with her and afraid she would leave him otherwise.
In the season 3 premiere, when Jimmy takes the chance (no pun intended) of ruining his relationship with Sabrina, just to tell her the truth. And she still accepts his marriage proposal.
The Chance's call in Barney to babysit Maw Maw while they're off at a couple's retreat. Right after they leave, he calls his mothers and has to call off his birthday brunch tomorrow because he thought being called over to watch Maw Maw was an excuse to get him to a surprise party. Over the episode Barney and Maw Maw bond, and it's quite touching how she tries to help him celebrate (not to mention hilarious when, after he passes out, she puts him in her bed and lets him come to conclusions the morning after). When the Chances all come back, they see Barney acting odd and leaving. After Maw Maw explains, Jimmy anxiously asks her if she told him about the big surprise party they've all set up for that night. She says of course not.
In "Squeak Means Squeak" Sabrina is challenged by Jimmy to take care of Hope for a weekend and not pass her off once the fun stuff was over. Sabrina was confident she could because Hope listened to her better than to Jimmy, but after that weekend has a minor breakdown over how much of a handful she can be, because now Hope doesn't listen to her. She finds out why when Hope calls her "Mommy". Sabrina's near Tears of Joy when hearing this, then hugging Hope afterwards just sells this moment.
Jimmy's narration during this moment is also very sweet, as he explains the trade-off that comes when a child knows you love them unconditionally is that they tend to be less likely to listen to you out of fear that you'll stop loving them.
Burt and Virginia doing everything they can to make sure Jimmy and Sabrina's wedding goes perfectly. It does, and few know how close it came to disaster.
At the end of the episode, Sabrina has a message for Jimmy on their wedding video. She knows Jimmy thinks he's so lucky to have HER, but she says SHE is the lucky one to have him, and Hope, and all his family. We're not sure if they got everything, as Burt was trying to destroy all the evidence that Lucy was alive and came to the wedding to kill Sabrina.
"Arbor Daze": The montage of Burt and Virginia going all out to celebrate all the holidays they could, just for little Jimmy.
During the "Arbor Day Future" portion of the Yet Another Christmas Carol plot involving Sabrina and the Ghost of Arbor Day (who also does other minor holidays), Sabrina smiles at seeing the preteen Hope and mentions how beautiful she is like a proud mother would.
Almost the entirety of "Mother's Day." Virginia was jealous that Sabrina gets Mother's Day rights from Hope, while she spent the first few years raising her (much like how she considers Maw Maw, her grandmother, to be her mother). Seeing how much it hurts her, Sabrina decides to pass Mother's Day rights from her own mom to Virginia, explaining that she has been more of a mom to her despite not actually having the title. While it involved a little deception to make her feel better (recruiting Frank and Shelley to fake a phone call, though that was because she never managed to get in touch with her biological mother) the last words has Sabrina saying "I'm with my family."
Sabrina: That's why I'm gonna keep the necklace that Hope made. 'Cause this one is one that I made for you. Happy Mother's Day.
Virginia: That's very sweet, but it's not Mother-in-Law's Day; it's Mother's Day. You should give that to your mother.
Sabrina: Over the last few years, you have been more of a mother to me than my mother ever was. I want you to have this.
Virginia: I see what you're doing, and it's very sweet, but—
Sabrina: What's my favorite color? What is it?
Sabrina: And you know that because?
Virginia: Because, for your wedding, you and I spent two days driving to every supermarket in town buying all the orange flowers.
Sabrina: And how did I chip my tooth?
Virginia: You thought you could skateboard drunk on Cinco de Mayo. And you not only chipped your tooth, you sprained your ankle.
Sabrina: And when did I start walking again?
Virginia: Three days later on Ocho de Mayo.
After her narcissistic gay father leaves again, the Chances and friends watch home videos of the real father figure Virginia had. Papa Wilfred.
Pretty much all of the "re-birthing" in "Adoption." Jimmy senses that Sabrina is uncomfortable with questions regarding her not being Hope's biological mother, even after officially adopting her she feels unfulfilled. The actual "re-birthing" is rather silly (and ends with an emergency c-section performed by Sabrina herself with a brick) but the gesture from Jimmy and the affection Hope gives her afterward brings her to tears. This shows that, while she may not have given birth to Hope, Hope sure sees Sabrina as her real mother.
From the series finale, the Call-Back to the Pilot when Kenny Loggins sings "Danny's Song" at Burt & Virginia's wedding. Also when there's a flashback of Virginia singing the song in the Pilot.
The way the whole story was brought full circle with Virginia's dad coming to stay with them and mend his relationship with her. Jimmy says it all, "You don't always become a parent at the perfect time." and no one on the show had a fairy tale experience, but that doesn't mean they aren't a loving family.
Burt's Happy Place includes a harem of beautiful women...all of whom are his wife, Virginia. Earlier in the series, he'd said that she's the only one for him, and that if she died, he wouldn't date or hook up with anyone else or remarry.